A rock is dropped from a sea cliff, and the sound of it striking the ocean is heard 2.9 s later. If the speed of sound is 340 m/s, how high is the cliff?
Answer:
h = 493 m
Explanation:
Given that,
A rock is dropped from a sea cliff, and the sound of it striking the ocean is heard 2.9 s later.
The total distance covered by the rock is 2d. We know that,
Speed = distance/time
\(v=\dfrac{2d}{t}\\\\d=\dfrac{vt}{2}\\\\d=\dfrac{340\times 2.9}{2}\\\\d=493\ m\)
So, the height of the cliff is equal to 493 m.
Please help me! As quickly as possible
Answer:
1. matter
2. kilograms
3. same
4. gravitational
5. gravity
6. space
7. weightlessness
8. Newton
9. weight
10. more
I HOPE THESE ARE CORRECT AND IT HELPS
a rod with uniform density (mass/unit length) 3 sin(x) lies on the -axis between 0 and pi find the mass and center of mass of the rod.
The center of mass of the rod is located at x = 0.5 on the -axis.
To find the mass of the rod, we need to integrate the density function over the length of the rod. We are given that the density of the rod is 3 sin(x) mass per unit length, and the length of the rod is from 0 to pi on the -axis. Therefore, the mass of the rod is:
M = ∫0π (3 sin(x)) dx
Using the integration formula for sin(x), we get:
M = [-3 cos(x)]0π
M = 3(cos(0) - cos(pi))
M = 6
So, the mass of the rod is 6 units.
Next, to find the center of mass of the rod, we need to find the position of the center of mass along the -axis. The position of the center of mass is given by the formula:
x_c = (1/M) ∫0π (x dm)
where x is the position of an infinitesimal element of the rod, and dm is the mass of that element. We can express dm as the product of the density function and the length element dx:
dm = ρ(x) dx = 3 sin(x) dx
Substituting dm into the formula for x_c, we get:
x_c = (1/M) ∫0π (x ρ(x) dx)
x_c = (1/6) ∫0π (x 3 sin(x) dx)
Using integration by parts with u = x and dv = 3 sin(x) dx, we get:
x_c = (1/6) [-x 3 cos(x) + 3 sin(x)]0π
x_c = (1/6) (0 - 0 + 3)
x_c = 0.5
Therefore, the center of mass of the rod is located at x = 0.5 on the -axis.
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12) Driving home from school one day, you spot a ball rolling out into the street (FIGURE 5-27). You brake for 1.20 s, slowing your 950-kg car from 16.0 m>s to 9.50 m>s. What was the average forceexerted on your car during braking and How far did you travel while braking?
We are given the following information
Mass of car = 950 kg
Initial speed of car = 16.0 m/s
Final speed of car = 9.50 m/s
Time = 1.20 s
The average force exerted on the car during braking can be found using Newton's 2nd law of motion
\(F=m\cdot a\)Where m is the mass of the car and a is the acceleration of the car.
The acceleration of the car is given by
\(\begin{gathered} a=\frac{v_f-v_i}{t} \\ a=\frac{9.50-16.0}{1.20} \\ a=-5.4167\; \; \frac{m}{s^2} \end{gathered}\)The negative sign indicates deacceleration since the car is stopping.
So, the force is
\(\begin{gathered} F=m\cdot a \\ F=950\cdot5.4167 \\ F=5145.865\; \; N \end{gathered}\)Therefore, an average force of 5145.865 N was exerted on your car during braking.
The distance traveled by the car while braking can be found as
\(s=v_i\cdot t+\frac{1}{2}\cdot a\cdot t^2\)Let us substitute the given values
\(\begin{gathered} s=16.0\cdot1.20+\frac{1}{2}\cdot(-5.4167)\cdot(1.20)^2 \\ s=19.20-3.90 \\ s=15.3\; m \end{gathered}\)Therefore, the car traveled a distance of 15.3 m while braking.
select the type of figurative language present in the following example:in leaves no step had trodden blacksymbolimagerymetaphorpersonification
The type of figurative language present in the example "in leaves no step had trodden black" is personification.
Personification is a figure of speech in which human qualities or actions are attributed to non-human entities. In the given example, the phrase "leaves no step had trodden black" personifies the leaves by suggesting that they have the ability to tread or walk.
By attributing the human action of stepping to the leaves, the poet gives them a sense of agency and animates them. This personification enhances the imagery of the poem, creating a vivid picture of untouched and unexplored surroundings, where the leaves have remained undisturbed.
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The figurative language present in the phrase 'In leaves no step had trodden black' is imagery. This phrase creates a visual image for the reader, contrasting with symbol, metaphor, and personification.
Explanation:The phrase 'In leaves no step had trodden black' from your question is an example of imagery. Imagery refers to language that appeals to one or more of the five senses. Here, this phrase creates a visual image of untouched leaves, helping the reader to more vividly imagine the scene being described. It does not suit the definitions of symbol, metaphor, or personification. A symbol represents itself and something else simultaneously, a metaphor makes a direct comparison between two unlike things, and personification assigns human traits to non-human entities or concepts. In this case, the leaves are not representing something else (symbol), not being compared directly with something else (metaphor), and not given human traits (personification).
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The anther and filament are parts of a flower's:
stamen
petal
pistil
stigma
Using the graph below answer the following questions about the Photo-electric effect.
a) What is the work function of the experimental photo-missive material?
b) What the threshold frequency of the experimental photo-missive material?
c) If the incoming frequency is 8.0 E14 Hz what would be the maximum kinetic energy of the most energetic electron?
d) If the incoming photon had a wavelength of 500.0 nm would you have a photo-electron ejected?
e) If you use a different experimental photo-missive material what would be the same on the graph?
f) What is the slope of the graph?
(a) The work function is 1.98 x 10⁻¹⁹ J.
(b) The threshold frequency is 3 x 10¹⁴ Hz.
(c) The maximum kinetic energy of the most energetic electron is 3.32 x 10⁻¹⁹ J.
(d) Photo-electron would be ejected.
(e) The only constant parameter would be speed of the photon.
(f) The slope of the graph is 6.67 x 10⁻³⁴ J.s
What is the work function of the experimental photo-missive material?(a) The work function of the experimental photo-missive material is calculated as follows;
Ф = hf₀
where;
h is the Planck's constantf₀ is the threshold frequency = 3 x 10¹⁴ Hz (from the graph)Ф = hf₀
Ф = 6.626 x 10⁻³⁴ x 3 x 10¹⁴
Ф = 1.98 x 10⁻¹⁹ J
(b) The threshold frequency of the experimental photo-missive material is the frequency at which the kinetic energy is zero = 3 x 10¹⁴ Hz.
(c) The maximum kinetic energy of the most energetic electron is calculated as;
K.E = E - Φ
K.E = ( 6.626 x 10⁻³⁴ x 8 x 10¹⁴) - 1.98 x 10⁻¹⁹ J
K.E = 3.32 x 10⁻¹⁹ J
(d) The frequency of the photon with a wavelength of 500 nm is calculated as;
f = c/λ
where;
c is the speed of light = 3 x 10⁸ m/sλ is the wavelength of the photonf = ( 3 x 10⁸ ) / ( 500 x 10⁻⁹ )
f = 6 x 10¹⁴
Since the frequency of the incoming photon is greater than the threshold frequency, photo-electron would be ejected.
(e) If you use a different experimental photo-missive material the only parameter that would be the same on the graph is speed of photon.
(f) The slope of the graph is calculated as;
m = (2.5 eV - 0 eV) / [(9 - 3) x 10¹⁴]
m = (2.5 ev) / (6 x 10¹⁴)
m = (2.5 x 1.6 x 10⁻¹⁹ ) / (6 x 10¹⁴ )
m = 6.67 x 10⁻³⁴ J.s
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If you have a 1000-element balanced binary search tree, what is the maximum number of comparisons that may be needed to find an element in the tree?
The maximum number of comparisons that may be needed to find an element in a 1000-element balanced binary search tree is 10.
To find an element in a balanced binary search tree, the maximum number of comparisons required is equal to the height of the tree.
In a balanced binary search tree with 1000 elements, the height can be calculated using the formula:
height = log2(n),
where n is the number of elements in the tree.
Therefore, the height of a balanced binary search tree with 1000 elements is approximately log2(1000) = 9.97.
Since the height of a tree must be an integer, we can round up the height to the nearest whole number, which in this case is 10.
Hence, the maximum number of comparisons that may be needed to find an element in a 1000-element balanced binary search tree is 10.
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4. Interference is an example of which aspect of electromagnetic radiation?
A) Particle behavior
B) photon behavior
C) the photoelectric effect
D) wave behavior
Answer:
D is the answer wave behavior
Interference, refraction, diffraction, and dispersion are all aspects of wave behavior. (D). That is, particles don't do these things.
Which type of modulation is used by remote-control toys?
amplitude
frequency
phase
pulse
Remote-control toys make use of pulse code modulation.
Which modulation type is used in radio-controlled toys?Pulse-width modulation (PWM), pulse-position modulation (PPM), and more recently spread-spectrum technology are used in typical radio control systems for radio-controlled models, and servomechanisms are used to activate the various control surfaces. Digital modulation is used in all current infrared remote control designs. Amplitude Shift Keying (ASK) and Frequency Shift Keying (FSK) are two fundamental types of digital modulation. (FSK).
What is the purpose of amplitude modulation?Electronic communication is where amplitude modulation is most commonly utilised. This method is being utilised in numerous communication channels, including computer modems, citizens band radio, VHF aviation radio, and portable two-way radios.
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a 62.0 kg box hangs from a rope. what is the tension in the rope if: part a. the box is at rest? part b. the box moves up a steady 4.90 m/s ? part c. the box has vy = 4.50 m/s and is speeding up at 5.50 m/s2 ? the y axis points upward. part d. the box has vy = 4.50 m/s and is slowing down at 5.50 m/s2 ?
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Question: A 62.0 Kg Box Hangs From A Rope. What Is The Tension In The Rope If: Part A. The Box Is At Rest? Part B. The Box Moves Up A Steady 4.90 M/S ? Part C. The Box Has Vy = 4.50 M/S And Is Speeding Up At 5.50 M/S2 ? The Y Axis Points Upward. Part D. The Box Has Vy = 4.50 M/S And Is Slowing Down At 5.50 M/S2 ?
A 62.0 kg box hangs from a rope. What is the tension in the rope if:
Part A. The box is at rest?
Part B. The box moves up a steady 4.90 m/s ?
Part C. The box has vy = 4.50 m/s and is speeding up at 5.50 m/s2 ? The y axis points upward.
Part D. The box has vy = 4.50 m/s and is slowing down at 5.50 m/s2 ?
A 62.0 kg box hangs from a rope. what is the tension in the rope. When the box is at rest, the tension in the rope is equal to the weight of the box When the box moves up at a steady speed of 4.90 m/s, the net force acting on the box is zero.
When the box is at rest, the tension in the rope is equal to the weight of the box. The weight of an object can be calculated by multiplying its mass by the acceleration due to gravity (g = 9.8 m/s^2). Therefore, the tension in the rope is given by:
Tension = Weight = mass * g = 62.0 kg * 9.8 m/s^2 = 607.6 N
Part B: When the box moves up at a steady speed of 4.90 m/s, the net force acting on the box is zero. The tension in the rope must balance the weight of the box. Therefore, the tension in the rope is equal to the weight of the box:
Tension = Weight = 62.0 kg * 9.8 m/s^2 = 607.6 N
Part C: When the box has a vertical velocity (Vy) of 4.50 m/s and is speeding up at 5.50 m/s^2, the net force acting on the box is the sum of the tension in the rope and the force due to the acceleration. The net force can be calculated using Newton’s second law (F = m * a):
Net Force = m * a = 62.0 kg * 5.50 m/s^2 = 341 N
To find the tension in the rope, we need to add the weight of the box to the net force:
Tension = Weight + Net Force = 62.0 kg * 9.8 m/s^2 + 341 N = 972.8 N
Part D: When the box has a vertical velocity (Vy) of 4.50 m/s and is slowing down at 5.50 m/s^2, the net force acting on the box is the difference between the tension in the rope and the force due to deceleration. The net force can be calculated using Newton’s second law:
Net Force = m * a = 62.0 kg * (-5.50 m/s^2) = -341 N (negative because it opposes the motion)
To find tOme tension in the rope, we subtract the net force from the weight of the box:
Kj Tension = Weight – Net Force = 62.0 kg * 9.8 m/s^2 – 341 N = 607.6 N
Therefore, the tension in the rope is 607.6 N in all cases, except for when the box is slowing down, where it is 972.8 N.
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A train was moving along east at 25 m/s, but brakes for 3 seconds, reducing its velocity to 13 m/s east.
What was its displacement while braking?
Answer:
57 m
Explanation:
Given:
v₀ = 25 m/s
v = 13 m/s
t = 3 s
FInd: Δx
Δx = ½ (v + v₀) t
Δx = ½ (13 m/s + 25 m/s) (3 s)
Δx = 57 m
Playing shortstop, you pick up a ground ball and throw it to second base. The ball is thrown horizontally with a speed of 13 m/s directly toward point A. When the ball reaches the second baseman 0,44 s later, it is caught at point B. How far were you from the second baseman? What is the distance of the vertical drop, the distance between point A and point B.
You were approximately 5.72 meters away from the second baseman. The vertical drop or distance between point A and point B was approximately 0.4576 meters.
To determine the distance between you (the shortstop) and the second baseman, we can use the formula for horizontal distance (d) traveled by an object moving at a constant horizontal velocity:
d = v * t
where:
- d is the horizontal distance traveled,
- v is the horizontal velocity of the ball,
- t is the time taken.
Given that the horizontal velocity (v) is 13 m/s and the time (t) is 0.44 s, we can calculate the horizontal distance (d) as follows:
d = 13 m/s * 0.44 s = 5.72 meters
So, you were approximately 5.72 meters away from the second baseman.
To find the vertical drop or the distance between point A and point B, we need to calculate the vertical component of the ball's motion. Since the ball is thrown horizontally, it will experience a constant vertical acceleration due to gravity.
The formula to calculate the distance (d) traveled vertically in free fall is:
d = 1/2 * g * t²
where:
- d is the vertical distance traveled,
- g is the acceleration due to gravity (approximately 9.8 m/s²),
- t is the time taken.
Given that the time (t) is 0.44 s, we can calculate the vertical distance (d) as follows:
d = 1/2 * 9.8 m/s² * (0.44 s)² = 0.4576 meters
So, the vertical drop or the distance between point A and point B is approximately 0.4576 meters.
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One of the most efficient engines ever built is a coal-fired steam turbine engine in the ohio river valley, driving an electric generator as it operates between 1,870°c and 430°c.
a. What is its maximum theoretical efficiency?
b. Its actual efficiency is 42.0%. How much mechanical power does the engine deliver if it absorbs 1.60 ✕ 10^5 J of energy each second from the hot reservoir?
A. The maximum theoretical efficiency is 67.2 %.
B. The hot reservoir is 56.7 kW.
Solution:
A. Max. theoretical (Carnot) efficiency = 1-T(cold)/T(hot)
or 1 - (430+273)/(1870+273) = 0.672 = 67.2 %.
B. mechanical power delivered = 0.42*1.35*10^5 = 56700 J/s = 56700 W = 56.7 kW.
A Carnot engine operating between two given temperatures exhibits the highest possible efficiency among heat engines operating between these two temperatures. The Carnot engine has the highest efficiency among heat engines operating between two temperatures. Diesel is more flammable than gasoline.
Second, petrol doesn't burn completely, so very little fuel is wasted. Because of this, diesel engines are more efficient than gasoline engines. The Carnot cycle achieves maximum efficiency because all heat is transferred to the working fluid at the highest temperature.
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If one travels away from the center of a mid-ocean rift (ridge) zone, the rock on either side of the rift zone gets progressively a. younger b. it stays the same age c. older d. depends on the nature of the rift zone e. none of the above
If one travels away from the center of a mid-ocean rift (ridge) zone, the rock on either side of the rift zone gets progressively younger.
Hence, the correct option is A.
When one travels away from the center of a mid-ocean rift zone (ridge), the rock on either side of the rift zone gets progressively younger.
This is because at the mid-ocean ridge, new oceanic crust is formed through volcanic activity. As tectonic plates move away from the ridge, new magma rises to fill the gap, solidifies, and forms new rock.
Therefore, the rocks farther away from the ridge are younger compared to the rocks closer to the ridge.
Hence, the correct option is A.
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Neglecting air resistance, which of the following statements is true regarding an object in freefall?Lector inmersivo A. An object’s acceleration increases at a constant rate. B. An object maintains a constant velocity. C. An object falls an equal distance in between each second. D. An object’s velocity and acceleration both increase at a constant rate. E. An object’s velocity changes at a constant rate, and its acceleration remains constant.
Answer:
E. An object’s velocity changes at a constant rate, and its acceleration remains constant.
Explanation:
When an object is in freefall, it implies that the object is falling freely under gravity. If it falls towards the earth surface, the fall is in the direction of the Earth's gravitational force.
At the point of release of the object, its initial velocity is zero because it is at rest. But when released, its velocity increases at a constant rate until it is acted upon by an external force. But its acceleration remains constant, acceleration due to gravity.
a diffraction pattern is formed on a screen 90 cm away from a 0.340-mm-wide slit. monochromatic 546.1-nm light is used. calculate the fractional intensity i/imax at a point on the screen 4.10 mm from the center of the principal maximum.
the fractional intensity i/imax at the point on the screen 4.10 mm from the center of the principal maximum is approximately 0.123.
The given parameters are:Width of the slit, d = 0.340 mm
Wavelength of the light, λ = 546.1 nm
Distance from the slit to the screen, L = 90 cm
Distance of the point on the screen from the center of the principal maximum, y = 4.10 mm
The distance between the center of the principal maximum and the first minima is given by:
ym = (m * λ * L) / d
Where m is the order of the minima
From the above equation, we can calculate the order of the minima closest to the given point on the screen as:
m = (y * d) / (λ * L) = (4.10 × 10^(-3) × 0.340 × 10^(-3)) / (546.1 × 10^(-9) × 90 × 10^(-2)) ≈ 1
The intensity at a point on the screen at distance y from the center of the principal maximum is given by the equation:
i / imax = [sin(πa sinθ / λ) / (πa sinθ / λ)]^2
where a is the width of the slit and θ is the angle between the line joining the point on the screen and the center of the principal maximum, and a line perpendicular to the slit at the point where the diffracted beam passes through the slit.θ can be approximated as:
θ ≈ (m * λ) / d = (1 × 546.1 × 10^(-9)) / 0.340 × 10^(-3) ≈ 1 × 10^(-3) radians≈ (180 / π) × (1 × 10^(-3)) degrees = 0.057296 degrees
Putting the values of θ and a in the equation for intensity, we get:
i / imax = [sin(πa sinθ / λ) / (πa sinθ / λ)]^2≈ [sin(π × 0.340 × 10^(-3) × (1 × 10^(-3)) / (546.1 × 10^(-9))) / (π × 0.340 × 10^(-3) × (1 × 10^(-3)) / (546.1 × 10^(-9)))]^2≈ 0.123
Thus, the fractional intensity i/imax at the point on the screen 4.10 mm from the center of the principal maximum is approximately 0.123.
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Like all planets, the planet Venus orbits the Sun in periodic motion and simultaneously spins about its axis. Just as on Earth, the time to make one complete orbit (i.e., the period of orbit) is what defines a year. And the time to make one complete revolution about its axis (i.e., the period of rotation) is what defines a day. The period of orbit for the Earth is 365.25 days and the period of rotation is 24 hours (1.00 day). But when these same values for Venus are expressed relative to Earth, it is found that Venus has a period of orbit of 225 days and a period of rotation of 243 days. So for Venus inhabitants, a day would last longer than a year! Determine the frequency of orbit and the frequency of rotation (in Hertz) on Venus. Ans: A marine weather station detects waves which are 9.28 meters long and 1.65 meters high and travel a distance of 50.0 meters in 21.8 seconds. Determine the speed and the frequency of these waves. Ans:
Answer:
a) F = 5.14 10⁻⁸ Hz, f = 4.76 10-8 Hz, b) v = 2.29 m / s, f = 42.5 Hz
Explanation:
a)This problem has two parts.
For the calculations relative to the planet Venus, we use that the period and the frequency are related
f = 1 / T
frequency of the orbit around the Sun
Let's reduce the period to the SI system
T = 225 days (24h / 1days) (3600 s / 1h) = 1.94 10⁷ s
F = 1 / 1.94 10⁷
F = 5.14 10⁻⁸ Hz
rotation frequency
T = 243 d = 2.1 107 s
f = 1 / T
f = 1 / 2.1 107
f = 4.76 10-8 Hz
b) give the data of some marine waves
the speed of the wave can be found with kinematics
v = x / t
v = 50.0 / 21.8
v = 2.29 m / s
If the wavelength is L = 9.28m
this distance is the distance between two consecutive ridges or valleys
λ / 2 = L
λ = 2L
λ = 2 9.28
λ = 18.56 m
the speed of the wave is
v = λ f
f = v /λ
f = 2.29 / 18.56
f = 42.5 Hz
a model rocket engine applies 1500 j of work launching a 0.80 kg model rocket straight up from rest over the first 35 meters of the flight how fast is it going when the engine cuts out?
The final velocity of the model rocket when the engine cuts out is \(32.3 m/s.\)
We may solve for the model rocket's final velocity using the formula: work done (W) = change in kinetic energy (KE). We must first identify the work the model rocket engine has done. It is stated that 1500 J of work are applied.
\(W = 1500 J\)
Next, we need to find the change in kinetic energy of the model rocket. We know that it starts from rest and travels 35 meters with a mass of 0.80 kg.
\(ΔKE = 1/2 mv^2 - 0\)
\(ΔKE = 1/2 (0.80 kg) v^2\)
\(ΔKE = 0.40v^2\)
Now we can substitute these values into the equation:
\(1500 J = 0.40v^2\)
Solving for v, we get:
\(v = \sqrt{1500 J / 0.40(0.80 kg}\)
\(v = 32.3 m/s\)
Therefore, the model rocket is going 32.3 m/s when the engine cuts out.
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If 5x instead of 10x oculars were used in your microscope with the same objectives, what magnifications would be achieved?
The magnification is doubled when 10x oculars are used instead of 5x in our microscope with the same objectives.
When multiple lenses are lined together, the overall magnification can be calculated by multiplying the individual magnifications of each lens.
M = M1 × M2 × M3 × ... × Mn
where M is the overall magnification and M1, M2, M3, ..., Mn are the magnifications of the individual lenses.
Let M be the magnification of the objective, then the overall magnification,
when 5x ocular is used,
M1 = M × 5
M1 = 5M
when 10x ocular is used
M2 = M × 10
M2 = 10M
Therefore, the magnification is doubled when 10x ocular is used instead of 5x in our microscope with the same objectives.
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the value of velocity ratiio is greater than the value of mechanical advantage
Answer:
The mechanical advantage of a machine is always less than its velocity ratio.It is because mechanical advantage decreases due to the friction and weight of moving parts of the machine, but the velocity ratio remains constant.
Suppose that an object is dropped from a height of hy meters and hits the ground with a velocity of v meters per second. Then v 1962 an object is dropped from a height of 269 meters, with what velocity does it hit the ground? Round your answer to the nearest tenth. meters per second
Answer:
The velocity at which it hit the ground is 72.6 meters.
Explanation:
The v1962 an object is dropped from a height of 269 meters.The Kinematic equation for free fall is v² = u² + 2gh.where v is the final velocity, u is the initial velocity, and g is the acceleration due to gravity.So,
h = 269 meters
u = 0 m/s ( 0 for a dropping object )
g = 9.8 m/s²
By Substitute the kinematic equation
v² = u² + 2gh
v² = 0 x 0 + 2 x 9.8 x 269
v² = 0 + 5272.4 => 5272.4
v = √5272.4
v = 72.6
Therefore the object is dropped from a height of 269 meters, it will hit the ground with a velocity of 72.6 meters per second.
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Suppose the moon rotated on its axis just as quickly as Earth. Would we still always see the same side of the moon from Earth?
Answer:
No, The Moon, on the other hand, rotates once around its every 28 days, and once around the Earth in that same 28 days. The result of this combination is that the same side of the Moon is always facing the Earth.
What ions are produced from acids and bases?
Answer:
Give person above me brainliest
Explanation:
As shown in the figure below, April enters a race. She runs leftward 100\,\text m100m100, start text, m, end text to her horse, then she rides 500\,\text m500m500, start text, m, end text to her truck, then she drives 1000\,\text m1000m1000, start text, m, end text in a total time of 120\,\text s120s120, start text, s, end text..
The average speed of April, given the data from the question is 13.33 m/s
What is speed?Speed is the distance travelled per unit. Mathematically, it can be expressed as:
Speed = distance / time
What is average speed?Average speed is simply defined as the total distance travelled divided by the total time taken to cover the distance .
Average speed = Total distance travelled / total time
How to determine the average speedFrom the question given above, the following data were obtained:
Total distance = 100 + 500 + 1000 = 1600 mTotal time = 120 sAverage speed =?Average speed = Total distance travelled / total time
Average speed = 1600 / 120
Average speed = 13.33 m/s
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Complete question
As shown in the figure below, April enters a race. She runs leftward 100 m to her horse, then she rides 500m to her truck, then she drives 1000m in a total time of 120s.What is her average velocity over the 120s period? What is her average speed over the 120s period?
Answer:
-13 | Velocity
13 | Speed
he tangent plane to the surface z= 53−x 2
−2y 2
at the point (3,2,6).
To explain the tangent plane to the surface, `z = 53 − x² − 2y²` at the point `(3, 2, 6)`, let us first determine the partial derivatives of `z` with respect to `x` and `y`.
Partial derivative of `z` with respect to `x`, `∂z/∂x = -2x`Partial derivative of `z` with respect to `y`, `∂z/∂y = -4y`Now, let's find the gradient vector `grad z` at `(3, 2, 6)` and the value of `z` at `(3, 2)`.gradient vector `grad z = (-2x, -4y, 1)`gradient vector `grad z = (-6, -8, 1)` at `(3, 2, 6)`.Value of `z` at `(3, 2)` is given by `z = 53 - 3² - 2(2)² = 39`.
Therefore, the equation of the tangent plane to the surface `
z = 53 − x² − 2y²` at `(3, 2, 6)` is:
`z - 6 = -6(x - 3) - 8(y - 2)`
which can be written as:`6x + 8y + z = 50`Thus, the equation of the tangent plane to the surface `z = 53 − x² − 2y²` at the point `(3, 2, 6)` is `6x + 8y + z = 50`.
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how much work does f with arrow do when the proton moves along the straight-line path from the point (0.10 m, 0) to the point (0.10 m, 0.3 m)?
The work done by force f on the proton is \(- 6.912 x 10^-34 J\).
The work done by force (f with arrow) when a proton moves along the straight-line path from the point (0.10 m, 0) to the point (0.10 m, 0.3 m) is given by:Work = Change in potential energy of the protonThis is because the force is conservative (i.e., it doesn't depend on the path taken by the proton).We know that the proton moves only along the vertical direction, therefore, its displacement is:∆x = 0and
∆y = 0.3 mThe potential energy of a proton is given by:
Potential energy = - q * V where
q = charge of proton (\(1.6 x 10^-19\) C)
V = potential difference between two points at which proton movesThe potential difference between the two points is given as follows:V = VB - VAwhere
VB = potential at point (0.10 m, 0.3 m)VA
= potential at point (0.10 m, 0)We can take
VA = 0 since we are considering it as reference level of potential energy.
The potential at point (0.10 m, 0.3 m) can be calculated as follows:We know that the electric field due to a point charge is given by:E = \(k * q / r^2\) where
k = Coulomb's constant (\(9 x 10^9 N.m^2.C^-2\))
q = charge of point charger
r = distance between point charge and point of interestThus, the electric field at point (0.10 m, 0.3 m) due to the charge is: E = \(k * q / r^2\) where
q = proton charge (\(1.6 x 10^-19\) C)
r = distance between proton and charge
= 0.1 mThus,
E = (\(9 x 10^9\)) * \((1.6 x 10^-19) / (0.1^2)\)
= \(1.44 x 10^-14\) N/CThe potential at point (0.10 m, 0.3 m) due to the charge is:
V = Edwhere
Ed = distance moved by proton
= ∆y
= 0.3 mThus,
\(V = 1.44 x 10^-14 * 0.3\)
= \(4.32 x 10^-15\) VTherefore, the potential difference between the two points is:
V = VB - VA
= \(4.32 x 10^-15 - 0\)
= 4.32 x 10^-15 JThus, the work done by force f on the proton is:
Work = Change in potential energy of the proton
= - q * (VB - VA)
\(= - (1.6 x 10^-19) * (4.32 x 10^-15)\)
\(= - 6.912 x 10^-34 J\).
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Hey you know these safety barriers you see on the freeway all the time? Explain the physics behind how the safety barriers help save lives during car accidents.
In the event of an accident or a car crash, road safety barriers and fences prevent automobiles from running off the road.
Which laws explain the physics behind the safety barriers and their use ?Newton's Three Laws of Physics can help explain what these safety barriers are and how they help to save lives during car accidents :
I. Unless acted upon by an imbalanced force, an object at rest will remain at rest, and an object at constant velocity will remain at constant velocity.
II. If an imbalanced force occurs, a mass will experience acceleration proportional to its magnitude.
III. When you apply a force to an object, you will feel a force that is equal in magnitude but opposite in direction.
What are the reasons for installing road safety barriers ?To protect and prevent out-of-control automobiles from entering other vehicles' lanes. As a result, the safety road barriers are installed in the middle of the road.To keep the automobiles from sliding down an incline. If there is a drop of 5 meters or more along the road, the road safety barriers should be put at one end of the road.To keep an out-of-control car from collapsing and colliding with a roadside obstacle. If there are numerous items along the road, such as large traffic signs, bridge piers, poles, and so on, safety road barriers should be built on one end of the road.Can learn more about safety barriers from https://brainly.com/question/17086354
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Two identical clocks are set to 12 noon time when on the ground at rest relative to the ground. One clock is placed in a spacecraft, sent into space and accelerated to a speed of v = 0.93 x 108 m/s. What will the moving clock read if the first clock reads 6 p.m.? Express your answer as the number of minutes from 6 pm.
First, for this problem, we will need to know the formula for time dilation
\(t=\frac{t_0}{\sqrt{1-\frac{v^2}{c^2}}}\)Where t is the time in the reference frame on earth
t0 is the time on the ship
v is the velocity relative to lightspeed
and c is light speed in a vacuum
For this problem, we will need to convert .93x10^8 to a fraction of light speed.
.93x10^8 = .31c
Now, we can plug in the numbers we get from the given
t0 = 6 hours since the ship has been in the air for 6 hours
\(t=\frac{6}{\sqrt{1-\frac{(.31c)^2}{c^2}}}\)t = 6.31089
For the answer to be valid, we will convert .31089 to minutes by multiplying it by 60 (60 minutes in a hour)
18.654 minutes
An object with more mass has more kinetic energy than an object with less
mass, if both objects are moving
OA) at the same speed
OB) in the same direction
OC) in opposite directions
Explanation:
The kinetic energy of an object is given in terms of its mass and object as :
\(K=\dfrac{1}{2}mv^2\)
An object with more mass has more kinetic energy. An object with less mass, if both objects are moving at the same speed, in opposite directions, will have less kinetic energy. The square of v will give positive number.