In an inelastic collision, two or more objects stick together and travel as one unit after the collision. The principle of conservation of momentum states that the total momentum of a closed system remains constant if no external forces act on the system, which is also true for an inelastic collision.
As a result, the momentum of the first cart is equal to the combined momentum of the two carts after the collision, since the collision is inelastic. The velocity of the two carts after the collision can be calculated using the conservation of momentum, as follows:0.400 kg x 0.22 m/s + 0 kg x 0 m/s = (0.400 kg + 0 kg) x 0.16 m/s0.088 Ns = 0.064 NsThe total momentum of the system is 0.064 Ns.
The two carts move together after the collision with a velocity of 0.16 m/s. The mass of the second cart is 0 kg, therefore, its initial momentum is 0 Ns. The momentum of the first cart is therefore equal to the total momentum of the system.
The initial momentum of the first cart can be calculated using the following formula:p = mv0.088 Ns = 0.400 kg x v Therefore, the initial velocity of the first cart is:v = p/mv = 0.088 Ns / 0.400 kgv = 0.22 m/s Hence, the initial velocity of the first cart is 0.22 m/s.
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In an experiment, a ringing bell is placed in a vacuum jar that does not have any air in it. What best describes why the bell is seen vibrating but not heard?
Answer:
C. Light does not need a medium to travel through, but since sound waves must have a medium to vibrate, sound is not created where no air is present.
Explanation:
The reason the bell is seen to vibrate but not heard is that unlike light, which does not require a medium to pass through, sound waves require an air-filled space in order to vibrate. Option C is correct.
What is a sound wave?A sound wave is produced when a medium begins to vibrate. When an entity vibrates, a pressure wave is formed, which causes sound.
Light does not need a medium to travel through, but since sound waves must have a medium to vibrate, the sound is not created where no air is present best describes why the bell is seen vibrating but not heard.
The complete question is attached.
Hence option C is correct.
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an electromagnetic wave has an electric field given by: e = i(225 v/m)sin[(0.077m-1 )z – (2.3 x 107 rad/s)t] what are the wavelength and frequency of the wave?
The wavelength (λ) of the electromagnetic wave is approximately 81.56 meters, and its frequency (f) is approximately 3.66 x 10^6 Hz.
e = i(225 V/m)sin[(0.077 m^(-1))z - (2.3 x 10^7 rad/s)t]
The equation contains two important terms: (0.077 m^(-1)) and (2.3 x 10^7 rad/s).
1. Wavelength (λ): The term (0.077 m^(-1)) represents the wave number (k), which is related to the wavelength as follows: k = 2π/λ. To find the wavelength, we can rearrange the formula:
λ = 2π/k = 2π/(0.077 m^(-1)) ≈ 81.56 m
2. Frequency (f): The term (2.3 x 10^7 rad/s) represents the angular frequency (ω), which is related to the frequency as follows: ω = 2πf. To find the frequency, we can rearrange the formula:
f = ω/(2π) = (2.3 x 10^7 rad/s)/(2π) ≈ 3.66 x 10^6 Hz
So, the wavelength (λ) of the electromagnetic wave is approximately 81.56 meters, and its frequency (f) is approximately 3.66 x 10^6 Hz.
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Someone please help.
Q. A body of mass 10kg falling freely in the gravitational field close to the moon's surface has an acceleration of 1.6 m/s.
what is the gravitational field strength on the moon?
A. 0 N/kg
B. 1.6 N/kg
C. 10 N/kg
D.16 N/kg
Answer:
B is the answer
Explanation:
What is the acceleration of the object?
whats the difference between transverse and longitudinal waves?
Answer:
longitudianl particles are dispelled parrell
Explanation:
transverse perpendicular
5. A 300-day old radioactive substance shows an activity of 5000 dps, 150 days later its activity becomes 2500 dp What was its initiactivity?
Answer:
In 150 days its activity drops from 5000 to 2500
This implies a half-life of 150 days
If the substance was measured at 300 days it had decayed thru 2 half-lives
Initially its activity was 4 * 5000 because 4 implies a decay of 2 half-lives
Initial activity = 4 * 5000 = 20,000
If u have it, u want to share it. If u share it u dont have it.
what is it?
I think its a secret!!
Answer:
uhh, uhh i think it's a carrot?
nah a secret
Explanation:
Current is a stream of
Answer:
water?
Explanation:
Find the magnitude of the resultant force and the angle it makes with the positive x-axis. (Let a = 20 lb and b= 14lb).
The magnitude of the resultant force is approximately 27.7 lb and the angle it makes with the positive x-axis is approximately 15.5°.
To find the magnitude of the resultant force and the angle it makes with the positive x-axis, we will use vector addition.
Let a = 20 lb and b = 14 lb. We first need to find the x and y components of the two vectors using trigonometry.Let α be the angle that the vector a makes with the positive x-axis. Then, we have:
cos α = adjacent/hypotenuse = 15/20 = 0.75
sin α = opposite/hypotenuse = 5/20 = 0.25
Hence, the x-component of vector a is:
ax = a cos α = 20 × 0.75 = 15 lb
And the y-component of vector a is:
ay = a sin α = 20 × 0.25 = 5 lb
Similarly, let β be the angle that the vector b makes with the positive x-axis. Then, we have:
cos β = adjacent/hypotenuse = 12/14 = 0.857
sin β = opposite/hypotenuse = 2/14 = 0.143
Hence, the x-component of vector b is:
bx = b cos β = 14 × 0.857 = 12 lb
And the y-component of vector b is:
by = b sin β = 14 × 0.143 = 2 lb
To find the resultant vector, we add the components of the two vectors:
Rx = ax + bx = 15 + 12 = 27 lb
Ry = ay + by = 5 + 2 = 7 lb
The magnitude of the resultant vector is given by the Pythagorean theorem as:
R = √(Rx² + Ry²) = √(27² + 7²) ≈ 27.7 lb
The angle that the resultant vector makes with the positive x-axis is given by the arctangent function as:
θ = arctan(Ry/Rx) = arctan(7/27) ≈ 15.5°
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When compared to winds at the surface, winds at 2,000 feet areA. higher due to absence of frictionB. higher and go at right angles to the isobars due to frictionC. higher because they move from an area of higher pressure to lower pressure
When compared to winds at the surface, winds at 2,000 feet are typically higher due to the absence of friction.
At the surface, winds are affected by friction with the Earth's surface, which slows them down and causes them to move in a more turbulent and erratic fashion. However, as winds move up in altitude, they encounter less and less friction, allowing them to increase in speed and flow in a more uniform and predictable manner.
While friction may still have some influence on winds at 2,000 feet, it is not as significant as at the surface. Therefore, winds at this altitude tend to move more smoothly and follow a more consistent path, often perpendicular to the isobars (lines of equal pressure) on a weather map. This makes them useful for aviation purposes, as pilots can use this information to plan their flight paths and take advantage of favorable tailwinds or avoid dangerous crosswinds.
In contrast, winds at the surface are more affected by local topography, temperature gradients, and other factors that can cause them to vary widely in direction and speed. Overall, winds at 2,000 feet are an important component of the Earth's atmospheric circulation system, and understanding their behavior is essential for predicting weather patterns and ensuring safe air travel.
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An Object with a mass o 5.13kg placed on top of a spring compresses it by 0.25m (a) what is the force constant of the spring (b) How high will this object go when the spring releases its energy?
The force constant of the spring is 200.696 N/m & The height the object achieves when the spring releases its energy is 2.5087 m
The spring constant is the force needed to stretch or compress a spring, divided by the compressive or expansive distance. It's used to determine stability or instability in the spring, and therefore the system it's intended for. we know,
F = kx
Therefore,
k = F/x
We also know that the force being exerted on the spring is equal to the mass of the object. Hence, F = mg = 5.13 * 9.8 N = 50.174 N and we know compression due to the mass is 0.25m. Therefore,
K = 50.174/0.25 N/m
K = 200.696 N/m
Therefore, The Spring Constant is 200.696 N/m
On release, the spring potential energy gets converted to kinetic energy. Hence, on release, the height attained by the object is given by:
h = \(1/2 kx^{2}\)
We know that k=200.696 N/m and x=0.25 m. Therefore the height is:
h = \(1/2 (200.696 N/m)(0.25 m)^{2}\)
h = 2.5087 m
Therefore, the force constant of the spring is 200.696 N/m & The height the object achieves when the spring releases its energy is 2.5087 m
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Two billiard balls of equal mass collide. Ball 1 is initially moving at 0.43 m/s to the left, and ball 2 is initially at rest. Which of the following sets of final velocities does not describe an inelastic collision between the balls?
A. Ball 1 at 0.12 m/s left, Ball 2 at 0.31 m/s left
B. Ball 1 at 0.21 m/s left, Ball 2 at 0.22 m/s left
C. Ball 1 at 0.10 m/s left, ball 2 at 0.33 m/s left
D. Ball 1 at rest, ball 2 at 0.43 m/s left
Answer: B
"Ball 1 at 0.21 m/s left, Ball 2 at 0.22 m/s left"
A ____ circuit sends a measured fluid flow directly back to the reservoir with the remaining pump output used to maintain actuator speed.
An open center circuit sends a measured fluid flow directly back to the reservoir with the remaining pump output used to maintain actuator speed.
An open center circuit is a hydraulic system that is used in heavy-duty construction machinery and similar applications. The open center circuit is a common configuration for hydraulic systems. This type of system enables the hydraulic oil to flow back to the reservoir, allowing it to cool down and re-enter the system at a later time.
Open center circuits use a three-position directional valve, which allows the fluid to bypass the hydraulic motor or cylinder when the valve is in the neutral position. The fluid that is not sent to the actuator is sent back to the reservoir, which enables the fluid to cool down and re-enter the system later.
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How may the stability of a body be increased?
Answer:
The functionality of a body can be restored with the help of appropriate flexibility and strengthening. Once everything is in place, you can exercise those muscles specifically for balance to put them to the test. Your body may then adjust, improving your general stability as you get better at completing those activities.
Answer:
The stability of an object is increased when the lower the centre of gravity is.
So we should try to lower the centre of gravity.
A 2kg water balloon is flying at a rate of 4m/s^2. With what force will it hit its target?
Explanation:
F=m×a
m=2kg
a=4m/s^2
F=2kg×4m/s^2
F=8N
A 2 kg water balloon is flying at a rate of 4 m/s². Force with which balloon will hit its target is 8 Newton.
What is force?A force is a push or pull upon an object resulting from the object's interaction with another object. Whenever there is body with some mass than there is force.
Given in the question mass and acceleration of balloon, force is given as
F = m*a
m = 2 kg
a = 4 m/s²
F = 2 kg×4 m/s²
F = 8 N
A 2 kg water balloon is flying at a rate of 4 m/s². Force with which balloon will hit its target is 8 Newton.
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A charge is divided q1 and (q-q1)what will be the ratio of q/q1 so that force between the two parts placed at a given distance is maximum?
Answer:
\(q / q_{1} = 2\), assuming that \(q_{1}\) and \((q - q_{1})\) are point charges.
Explanation:
Let \(k\) denote the coulomb constant. Let \(r\) denote the distance between the two point charges. In this question, neither \(k\) and \(r\) depend on the value of \(q_{1}\).
By Coulomb's Law, the magnitude of electrostatic force between \(q_{1}\) and \((q - q_{1})\) would be:
\(\begin{aligned}F &= \frac{k\, q_{1}\, (q - q_{1})}{r^{2}} \\ &= \frac{k}{r^{2}}\, (q\, q_{1} - {q_{1}}^{2})\end{aligned}\).
Find the first and second derivative of \(F\) with respect to \(q_{1}\). (Note that \(0 < q_{1} < q\).)
First derivative:
\(\begin{aligned}\frac{d}{d q_{1}}[F] &= \frac{d}{d q_{1}} \left[\frac{k}{r^{2}}\, (q\, q_{1} - {q_{1}}^{2})\right] \\ &= \frac{k}{r^{2}}\, \left[\frac{d}{d q_{1}} [q\, q_{1}] - \frac{d}{d q_{1}}[{q_{1}}^{2}]\right]\\ &= \frac{k}{r^{2}}\, (q - 2\, q_{1})\end{aligned}\).
Second derivative:
\(\begin{aligned}\frac{d^{2}}{{d q_{1}}^{2}}[F] &= \frac{d}{d q_{1}} \left[\frac{k}{r^{2}}\, (q - 2\, q_{1})\right] \\ &= \frac{(-2)\, k}{r^{2}}\end{aligned}\).
The value of the coulomb constant \(k\) is greater than \(0\). Thus, the value of the second derivative of \(F\) with respect to \(q_{1}\) would be negative for all real \(r\). \(F\!\) would be convex over all \(q_{1}\).
By the convexity of \(\! F\) with respect to \(\! q_{1} \!\), there would be a unique \(q_{1}\) that globally maximizes \(F\). The first derivative of \(F\!\) with respect to \(q_{1}\!\) should be \(0\) for that particular \(\! q_{1}\). In other words:
\(\displaystyle \frac{k}{r^{2}}\, (q - 2\, q_{1}) = 0\).
\(2\, q_{1} = q\).
\(q_{1} = q / 2\).
In other words, the force between the two point charges would be maximized when the charge is evenly split:
\(\begin{aligned} \frac{q}{q_{1}} &= \frac{q}{q / 2} = 2\end{aligned}\).
a uniform helicopter rotor blade is 7.80 m long, has a mass of 110 kg, and is attached to the rotor axle by a single bolt. (a) what is the magnitude of the force on the bolt from the axle when the ro- tor is turning at 320 rev/min? (hint: for this calculation the blade can be considered to be a point mass at its center of mass. why?) (b) calculate the torque that must be applied to the rotor to bring it to full speed from rest in 6.70 s. ignore air resistance. (the blade cannot be considered to be a point mass for this calculation. why not? assume the mass distribution of a
This might sound like a school assignment, but it actually demonstrates the forces acting on a rotor hub. Considering that the Cof G is halfway up the blade, or 3.9 m, the G force will operate on the blade.
What does a force mean in science?Science has a particular definition for the word "force." Using the terms "push" or "pull" to describe a force at this level is perfectly acceptable. . A force from some other thing is felt by something else. A force is a force, regardless of whether anything is alive or not.
They define force and example.A body's propensity to modify to change its structure as a reaction of an external factor is referred to as "force." The body may also change in size, shape, or direction as a result of a force being applied to it. A 448 G force is calculated to be applied to its blade. Correct: 400 for Six!
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At time t=​0, a particle is located at the point ​(1​,1​,3​). It travels in a straight line to the point ​(5​,9​,4​), has speed 6 at ​(1​,1​,3​) and constant acceleration 4i+8j+k. Find an equation for the position vector r​(t) of the particle at time t.
Ignoring the malformed character, it looks like you're saying you have particle initially located at (1, 1, 3) that travels in a straight line to (5, 9, 4) with initial speed 6 and constant acceleration vector 4i + 8j + k.
Use the fundamental theorem of calculus to determine the velocity function for the particle:
\(\vec v(t) = \vec v(0) + \displaystyle \int_0^t \vec a(u) \, du\)
The particle moves in the same direction as the vector
(5i + 9j + 4k) - (i + j + 3k) = 4i + 8j + k
which has magnitude
√(4² + 8² + 1²) = √81 = 9
Normalize the direction vector by dividing it by its magnitude:
(4i + 8j + k)/9 = 4/9 i + 8/9 j + 1/9 k
The particle has initial speed 6, so we must scale this unit vector by a factor of 1/6 to get the initial velocity vector:
6 (4/9 i + 8/9 j + 1/9 k) = 8/3 i + 16/3 j + 2/3 k
Solve for v(t) :
\(\vec v(t) = \dfrac83\vec\imath + \dfrac{16}3\vec\jmath + \dfrac23\vec k + \displaystyle \int_0^t \left(4\vec\imath + 8\vec\jmath+\vec k\right) \, du\)
\(\vec v(t) = \dfrac83\vec\imath + \dfrac{16}3\vec\jmath + \dfrac23\vec k + \left(4t\,\vec\imath + 8t\,\vec\jmath+t\,\vec k\right)\)
\(\vec v(t) = \left(\dfrac83+4t\right)\vec\imath + \left(\dfrac{16}3+8t\right)\vec\jmath + \left(\dfrac23+t\right)\vec k\)
Use the fundamental theorem again to find the position vector r(t) :
\(\vec r(t) = \vec r(0) + \displaystyle \int_0^t \vec v(u) \, du\)
\(\vec r(t) = \vec\imath+\vec\jmath+3\vec k + \displaystyle \int_0^t \left(\left(\dfrac83+4u\right)\vec\imath + \left(\dfrac{16}3+8u\right)\vec\jmath + \left(\dfrac23+u\right)\vec k\right) \, du\)
\(\vec r(t) = \vec\imath+\vec\jmath+3\vec k + \left(\left(\dfrac83 t+2t^2\right)\vec\imath + \left(\dfrac{16}3t+4t^2\right)\vec\jmath + \left(\dfrac23t+\dfrac12t^2\right)\vec k\right)\)
\(\vec r(t) = \left(1+\dfrac83 t+2t^2\right)\vec\imath + \left(1+\dfrac{16}3t+4t^2\right)\vec\jmath + \left(3+\dfrac23t+\dfrac12t^2\right)\vec k\)
Which of the following nuclei is likely to release energy when undergoing nuclear fusion?
a. iron-56
b. uranium-235
c. plutonium-239
d. deuterium
Deuterium is likely to release energy when undergoing nuclear fusion. Deuterium is an isotope of hydrogen that contains one proton and one neutron in its nucleus. Fusion occurs when two light nuclei, such as deuterium, combine to form a heavier nucleus, such as helium. This process releases a large amount of energy, which is the basis for how the sun and other stars produce energy.
Iron-56, uranium-235, and plutonium-239 are not likely to release energy through nuclear fusion. Iron-56 has the highest binding energy per nucleon, which means that it requires energy input to fuse with another nucleus. Uranium-235 and plutonium-239 undergo nuclear fission, which involves splitting a heavy nucleus into lighter nuclei and releasing energy.
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If 600 J of work was done to move a 40 kg object 8m how much force was applied to the
object?
Answer:
75 N
Explanation:
W = 600 J
x = 8 m
Plug those values into the following equation:
W = Fx
600 J = F(8m)
F = 75 N
The S.I. unit of E is NC^-1 and that of B is NA^-1 m^-1, then unit of E/B is
The S.I. unit of E is NC^-1 and that of B is NA^-1 m^-1, then unit of E/B is A m/C (ampere meter per coulomb). This unit represents the ratio between the electric field and the magnetic field, indicating the strength and direction of the electromagnetic field.
The SI unit of electric field (E) is NC^(-1) (newton per coulomb) and the SI unit of magnetic field (B) is NA^(-1) m^(-1) (tesla). To determine the unit of E/B, we need to divide the unit of E by the unit of B.
Dividing the unit of E (NC^(-1)) by the unit of B (NA^(-1) m^(-1)), we can simplify the expression:
E/B = (NC^(-1))/(NA^(-1) m^(-1))
To simplify this expression, we can cancel out the common units in the numerator and denominator:
E/B = (N/C)/(N/(A m))
Now, let's simplify further by dividing the numerator and denominator:
E/B = (N/C) * (A m/N)
Canceling out the common units:
E/B = (A m)/(C)
Therefore, the unit of E/B is A m/C (ampere meter per coulomb).
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Four resistors R1= 2. 00 ohms, R2= 2. 00 ohms, and R3= 2. 00 ohms, are connected in parallel. The battery has a voltage of 5V. Determine the equivalent resistance and current through the circuit
The equivalent resistance of the circuit is 0.67 ohms. The current through the circuit is 7.46 amps.
1/Req = 1/R1 + 1/R2 + 1/R3 + ...
In this case, we have three resistors connected in parallel, so:
1/Req = 1/R1 + 1/R2 + 1/R3
1/Req = 1/2.00 + 1/2.00 + 1/2.00
1/Req = 1.5
Req = 0.67 ohms
the equivalent resistance of the circuit is 0.67 ohms.
I = V/R
In this case, the voltage is 5V and the resistance is 0.67 ohms, so:
I = 5/0.67
I = 7.46 amps
Resistance is the measure of an object's ability to impede the flow of electric current through it. It is measured in ohms (Ω). Resistance is determined by the physical properties of an object, such as its dimensions, material, and temperature. When electric current flows through a conductor, it encounters resistance that slows down its flow. This resistance is caused by the collisions between electrons and the atoms in the conductor. The greater the number of collisions, the higher the resistance.
Resistance can be affected by changes in the physical properties of the conductor, such as length, cross-sectional area, or temperature. A longer or narrower conductor will have higher resistance, while a wider conductor will have lower resistance. The resistance of most materials increases with temperature. Understanding resistance is important for designing and operating electrical circuits. By controlling the resistance of a circuit, engineers can ensure that the correct amount of current flows to power the devices connected to it.
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When James sprayed liquid deodorant under his arm, the spot felt cold. Which sentence best explains why? A. The deodorant evaporates as it absorbs thermal energy from James’s skin. B. The deodorant condenses as it absorbs thermal energy from James’s skin. C. The deodorant evaporates as it transfers thermal energy to James’s skin. D. The deodorant evaporates as it absorbs temperature from James’s skin. E. The deodorant is a liquid that freezes at room temperature and pressure.
A. The deodorant evaporates as it absorbs thermal energy from James’s skin
What is heat transfer by conduction?
Conduction heat transfer is the transfer of heat by means of molecular excitement within a material without bulk motion of the mater.
Heat transfer process that takes place when the liquid deodorant is sprayed.
When James sprayed liquid deodorant under his arm, the deodorant evaporates as it absorbs thermal energy from James’s skin. This process caused the spot the feel cold.
Thus, the sentence that best explain the process is "The deodorant evaporates as it absorbs thermal energy from James’s skin".
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A 100 kg box is on an incline of 60°
What is the frictional force if the coefficient of friction is .2?
If the coefficient of friction is.2, the frictional force is 100 N.
The resistive force of friction (Fr) divided by the normal or perpendicular force (N) pushing the objects together yields the coefficient of friction (fr), which is a numerical value. The formula fr = Fr/N serves as a representation of it.
F = N is the equation for frictional force. Let's use the 2-kg block of wood that is resting on a table to be pushed from rest as an example. The static friction coefficient is taken into account in this situation. The static coefficient of wood is 0.5.
Calculation:F = μN
F = 2 × 100 ×cos60°
F = 200 × 1/2
F = 100 N
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When a wind-up toy is set in motion, elastic potential energy that was stored in a compressed spring is converted into the __________ of the toy’s moving parts
Answer:When a wind-up toy is set in motion, elastic potential energy that was stored in a compressed spring is converted into the kinetic energy of the toy's moving parts.
Explanation:
according to past research, why have women engaged in token resistance? group of answer choices they said no but then changed their minds and said yes.
According to past research, women have engaged in token resistance, which means they said no but then changed their minds and said yes. This occurs because of the cultural expectations that women are supposed to resist sexual advances even if they want to participate.
Because of this, women may feel pressure to refuse initially to maintain their reputation and avoid being seen as promiscuous. However, once the partner persists, they may give in to avoid being seen as too difficult or cold-hearted. Research has indicated that these behaviours are particularly evident in situations where the individual feels vulnerable or feels that they are in a low-power position. Women may also engage in token resistance to test their partner's sincerity and willingness to respect their boundaries. Additionally, it's worth noting that token resistance does not apply only to women, as men may also engage in this behaviour.
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A boy on his skateboard is accelerating at a rate of 5 m/s2 and has a mass of 40kg. How much force does the boy on his skateboard have?
Answer:
The answer is 200 NExplanation:
The force acting on an object given it's mass and acceleration can be found by using the formula
force = mass × acceleration
From the question we have
force = 40 × 5
We have the final answer as
200 NHope this helps you
According to the Big Bang theory
a. dark matter is changing to ordinary matter throughout the universe.
b. dark energy is pulling the universe into black holes.
c. the universe will someday end because of a "big bang."
d. the universe began with an enormous explosion.
Answer:
D. the universe began with an enormous explosion.
Explanation:
This theory states that the universe began as a single hot, dense, and small point. It then exploded, expanded, became less dense, and the temperature became cooler.
Hope this helps! :)
A satellite of mass 1.02 metric tons orbits Earth at a constant height. If the mass of Earth is 6 x 10^24 kg,its radius is 6,360 km,and the gravitational force between Earth and the satellite is 6.6 x 10^3 N, find the height of the satellite’s orbit rounded to the nearest kilometer. Take the universal gravitational constant, G = 6.67 x 10^-11 Nm^2/kg^2.
Answer:
height = 1.5 x 10⁶ m = 1500 km
Explanation:
We can use the formula of gravitational force from the Newton's Gravitational Law:
\(F = \frac{Gm_{1}m_{2}}{r^2}\)
where,
F = Gravitational Force = 6.6 x 10³ N
G = Universal Gravitational Constant = 6.67 x 10⁻¹¹ N.m²/kg²
m₁ = mass of earth = 6 x 10²⁴ kg
m₂ = mass of satellite = (1.02 tons)(1000 kg/1 ton) = 1.02 x 10³ kg
r = distance between center of earth and satellite = ?
Therefore, using these values in the equation, we get:
\(6.6\ x\ 10^3\ N = \frac{(6.67\ x\ 10^{-11} N.m^2/kg^2)(6\ x\ 10^{24} kg)(1.02\ x\ 10^3\ kg)}{r^2}\\\\r^2 = \frac{(6.67\ x\ 10^{-11} N.m^2/kg^2)(6\ x\ 10^{24} kg)(1.02\ x\ 10^3\ kg)}{6.6\ x\ 10^3\ N}\\\\\)
\(r = \sqrt{61.84\ x\ 10^{12}\ m^2 }\)
\(r = 7.86\ x\ 10^6 m\)
The distance between center of earth and the satellite is equal to the sum of height of satellite and radius of earth:
\(r = height + radius\ of\ earth\\7.86\ x\ 10^6 m = height + 6.36\ x\ 10^6 m\\height = 7.86\ x\ 10^6 m - 6.36\ x\ 10^6 m\)
height = 1.5 x 10⁶ m = 1500 km
If it is 2:00 AM at 90 East longitude, what time is it at 75 East longitude? 11. If it is 8:00 PM at 15 East, what time is it at 135 East longitude? 12. How many hours difference is there between 105 West longitude and the Prime Meridian? 13. If it is 9:30 AM in New York which is located 41 North Latitude, and 75 West Longitude, what t is it in Lima Peru which is located at 15 South latitude, and 75 West Longitude?
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11.The time at 75° East longitude would be 1 hour and 20 minutes behind. 12.The time at 135° degrees East longitude would be 4 hours ahead. and 13. the time in Lima, Peru (15° South latitude, 75° West longitude) would also be 9:30 AM.
At 2:00 AM at 90° East longitude, the time at 75° East longitude would be 1 hour and 20 minutes behind. This is because for every 15 degrees of longitude, there is a time difference of approximately 1 hour. Since the two longitudes in question have a difference of 15 degrees, we can divide this by 15 to calculate the time difference.
If it is 8:00 PM at 15° East longitude, the time at 135° East longitude would be 4 hours ahead. Similarly, for every 15 degrees of longitude, there is an approximate time difference of 1 hour. Since the two longitudes in question have a difference of 120 degrees, we can divide this by 15 to calculate the time difference.
There is a 7-hour difference** between 105° West longitude and the Prime Meridian (0° longitude). The Prime Meridian, passing through Greenwich, England, serves as the reference point for determining time zones. As one moves westward from the Prime Meridian, each 15 degrees of longitude corresponds to a time difference of approximately 1 hour. Therefore, the time at 105° West longitude would be 7 hours behind the time at the Prime Meridian.
If it is 9:30 AM in New York (41° North latitude, 75° West longitude), the time in Lima, Peru (15° South latitude, 75° West longitude) would also be 9:30 AM. The latitude does not affect the time difference between the two locations. However, since both locations have the same longitude (75° West), they would experience the same local time. The time difference between different latitudes is primarily significant for determining time zones rather than the actual time within a specific time zone.
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