A cube with an electric field passing through it is shown on the right. If the energy per time is 8 watts and the size of the cube is 10m x 10m x 10m, then the strength of the electric field, e0 is\(4π * 10^-7 Tm/A\) .
The size of the cube is given to be 10m x 10m x 10m. The energy per time is given to be 8 watts. Electric field strength is determined by dividing the energy density by the electric field. According to the given equation: Energy per time = Energy density × Volume Therefore, Energy density = Energy per time / Volume Energy density = 8 watts / (10 m x 10 m x 10 m)Energy density = 0.008 W/m^3.
The formula for electric field strength is given as:E = √(2 * energy density / ε0)Where ε0 is the permittivity of free space. Substitute the given values to find the electric field strength: E = √\((2 * 0.008 W/m^3 / 8.85 x 10^-12 Tm/A)E = √(2.263 x 10^9)E = 4.756 x 10^4 Tm/A\) The strength of the electric field, e0 is \(4π * 10^-7 Tm/A.\)
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What is the acceleration of a car making a turn in a circle with a 100m radius traveling at
17m/s?
Answer:
2.89 m/s²
Explanation:
From the question given above, the following data were obtained:
Radius (r) = 100 m
Velocity (v) = 17 m/s
Acceleration (a) =.?
The acceleration of a circular motion is defined by:
a = v²/r
Where:
a is the acceleration.
v is the velocity.
r is the radius.
With the above formula, we can obtain the acceleration of the car as follow:
Radius (r) = 100 m
Velocity (v) = 17 m/s
Acceleration (a) =.?
a = v²/r
a = 17²/ 100
a = 289/100
a = 2.89 m/s²
Therefore, the acceleration of the car is 2.89 m/s²
Alfred is studying a substance that is made out of only one element. This means that
Answer: A pure substance is something that occurs in nature. An element is made up of one type of atom only and cannot be split further. A compound has the combined properties of the elements from which it is made. Atoms show the macro properties of an element.
A wave has a speed of 20 m/s and a wavelength of 5 meters. if the same wave was created in the same medium, with half the original frequency, how would the wavelength change?
Answer:
The wavelength of the wave would increase to 10 meters.
Explanation:
We can use the formula:
velocity = frequency × wavelength
to relate the velocity, frequency, and wavelength of a wave.
Given that the wave has a speed of 20 m/s and a wavelength of 5 meters, we can solve for its frequency as follows:
frequency = velocity ÷ wavelength = 20 m/s ÷ 5 meters = 4 Hz
Now, if the same wave is created in the same medium, but with half the original frequency, its new frequency will be:
new frequency = 4 Hz ÷ 2 = 2 Hz
To find the new wavelength of the wave, we can rearrange the formula above to solve for wavelength:
wavelength = velocity ÷ frequency
Using the new frequency of 2 Hz, we get:
new wavelength = 20 m/s ÷ 2 Hz = 10 meters
Therefore, if the same wave was created in the same medium, with half the original frequency, the wavelength of the wave would increase to 10 meters.
Question 2:
Draw the following scenario: A 10μF capacitor is charged to 5V.
At time t = 0, a current of 2μA begins to flow out of the capacitor
through a resistor.
2a) Plot and measure the voltage o
A capacitor is a device that stores electrical energy in an electric field. The unit of capacitance is farads (F). A 10μF capacitor charged to 5V implies that\(Q = CV, where C = 10μF and V = 5V, therefore Q = (10 × 10^-6) × 5 = 50μC.\)
The voltage across the capacitor is maximum since it is fully charged. At time t = 0, a current of 2μA starts to flow out of the capacitor through a resistor. The voltage across the capacitor starts to decrease as a result of the current. The voltage across the capacitor varies with time.
The voltage across a capacitor is given by the equation below:V = V₀e^(-t/RC), whereV₀ is the initial voltage on the capacitor. R is the resistance of the resistor and C is the capacitance of the capacitor. t is time measured in seconds.Since the voltage across the capacitor is 5V, we substitute \(V₀ with 5V. RC = 10 × 10^-6 × R, therefore V = 5e^(-t/10R). To plot the graph, we set R equal to 1kΩ.\)
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where are Ascaris and Arthropods found ?class 10
Answer:
Ascaris and Arthropods are both types of organisms found in the animal kingdom. Ascaris are parasitic worms, commonly referred to as roundworms, which can be found in warm climates all over the world. Arthropods, on the other hand, are a large group of animals, including insects, arachnids, and crustaceans, that typically have jointed legs and a hard exoskeleton. Arthropods are found in almost all environments, from oceans to deserts to the tops of mountains.
Explanation:
For an Ultrasonic Vaporizer Us Duty Rate 4.2%, valued in USD$750, transported via Air and no valid CUSMA certificate available calculate: - Duty Charge - MPF - HMF
2. Same Ultrasonic Vaporizer Us Duty Rate 4.2%, valued in USD$750, transported via Ocean and no valid CUSMA certificate available calculate:
Duty Charge
MPF
HMF
1. The duty charge, MPF and HMF for the Ultrasonic Vaporizer transported via air are USD$31.50, USD$2.60 and USD$0.94, respectively.
2. The duty charge, MPF and HMF for the Ultrasonic Vaporizer transported via ocean are USD$31.50, USD$0.94 and USD$0.94, respectively.
How to calculate duty charge, MPF and HMFFor the Ultrasonic Vaporizer transported via air
Duty Charge:
Given information;
Duty rate = 4.2%
Value of goods = USD$750
Duty charge = Value of goods x Duty rate
Duty charge = USD$750 x 4.2%
Duty charge = USD$31.50
Merchandise Processing Fee (MPF)
MPF rate = 0.3464% (as of 2021)
Value of goods = USD$750
MPF = Value of goods x MPF rate
MPF = USD$750 x 0.3464%
MPF = USD$2.60
Harbor Maintenance Fee (HMF)
HMF rate = 0.125% (as of 2021)
Value of goods = USD$750
HMF = Value of goods x HMF rate
HMF = USD$750 x 0.125%
HMF = USD$0.94
Therefore, the total import fees for the Ultrasonic Vaporizer transported via air are:
Duty charge = USD$31.50
MPF = USD$2.60
HMF = USD$0.94
For the Ultrasonic Vaporizer transported via ocean
Duty Charge:
Given information:
Duty rate = 4.2%
Value of goods = USD$750
Duty charge = Value of goods x Duty rate
Duty charge = USD$750 x 4.2%
Duty charge = USD$31.50
Merchandise Processing Fee (MPF)
MPF rate = 0.125% (as of 2021)
Value of goods = USD$750
MPF = Value of goods x MPF rate
MPF = USD$750 x 0.125%
MPF = USD$0.94
Harbor Maintenance Fee (HMF):
HMF rate = 0.125% (as of 2021)
Value of goods = USD$750
HMF = Value of goods x HMF rate
HMF = USD$750 x 0.125%
HMF = USD$0.94
Therefore, the total import fees for the Ultrasonic Vaporizer transported via ocean are:
Duty charge = USD$31.50
MPF = USD$0.94
HMF = USD$0.94
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Duty Charge=$31.50
The MPF will be $27.23.
The HMF rate is $0.125 per metric ton.
Ultrasonic Vaporizer transported via Air:
Duty Charge: $31.50
MPF: $26.79
HMF: Not applicable
Ultrasonic Vaporizer transported via Ocean:
Duty Charge: $31.50
MPF: $27.23
HMF: HMF rate and weight of the vaporizer are needed to calculate the HMF.
Ultrasonic Vaporizer transported via Air:
Duty Charge: The duty charge is calculated by multiplying the value of the product ($750) by the duty rate (4.2%): Duty Charge = \(\$750 * 4.2\%\)
= \(\$31.50.\)
MPF: The MPF for air transport is based on the value of the merchandise. As the value of $750 is below the maximum, the MPF will be $26.79.
HMF: The HMF is not applicable for air transport.
Ultrasonic Vaporizer transported via Ocean:
Duty Charge: The duty charge is calculated in the same way as for air transport: Duty Charge = \(\$750 * 4.2\%\)
= \(\$31.50\).
MPF: The MPF for ocean transport is also based on the value of the merchandise. As the value of $750 is below the maximum, the MPF will be $27.23.
HMF: The HMF is applicable for ocean transport. The HMF rate is $0.125 per metric ton. The weight of the Ultrasonic Vaporizer is needed to calculate the HMF.
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Jain applies a input force of 100 N to a lever that has a Mechanical advantage of 3. What is the output force
Answer:
Output force = 300 N
Explanation:
Given that,
The mechanical advantage of a lever, m = 3
Input force, \(F_i=100\ N\)
We need to find the output force. The ratio of output force to the input force is called the mechanical advantage of the lever. So,
\(m=\dfrac{F_o}{F_i}\\\\F_o=m\times F_i\\\\F_o=3\times 100\\\\F_o=300\ N\)
So, the output force is 300 N.
three particles are fixed in place. the mass of b is greater than the mass of c. can a fourth particle (particle d) be pplaces somewhere so that the net gravitational force on particle a from particles b, c, and d is zero?
Its position of this particle D must be near the positive y-axis in the second meiotic division of the aforementioned equations.
What is gravitational force and example?This attraction that earth has on an object is referred to as gravitational force. Examples of motion brought on by gravitational force also include upwards motion of a ball being thrown, the downward motion of water moving through a stream, and the pull of gravity on river flow.
Briefing:When two bodies are separated by a distance R and have masses M and m, the gravitational attraction between them is:
F= GMm/R²
The gravitational force is a result of the interaction between the gravitational forces exerted by particle B and particle C on particle A.
We can claim that because particle B has a larger mass than particle A does, the gravitational force was closer to and roughly equal to the mass of the bodies.
The net gravitational force on particle A would be zero if particle D force is exerted that is equal to it and opposite to the normal Force that results.
As a result, particle D need to be positioned close to the positive y-axis in the second quadrant.
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A flashlight is 40.0 cm from a double convex lens. The image of the flashlight is
observed at a position 30.0 cm on the other side of the lens. What is the focal length
of the lens?
1) 0.0580cm
2) 10.0cm
3) 13.3cm
4) 17.2cm
Answer: 4.) 17.2cm
Explanation:
A flashlight is 40.0 cm from a double convex lens. The image of the flashlight is observed at a position 30.0 cm on the other side of the lens. What is the focal length?
Given the following :
Object distance(u) = 40cm
image distance (v) = 30cm
Focal length(f) =?
Using the mirror formular:
f = uv / (v+u)
f = (40 * 30) / (40 + 30)
f = 1200 / 70
f = 17.142857 cm
State two units bigger than kilogram and how are they related to kilogram
Answer:
quintal and metric tone.
Explanation:
1 quintal= 100kg
1 metric =1000kg
quintal measures mass of cars, trucks etc, but metric measures bigger things like cargo ships
hope it helps
A vehicle accelerates to 18.84 m/s after being stopped at a red light. The vehicle travels 29.26 m while accelerating from the intersection. How fast was its acceleration?
The acceleration of the vehicle is 6.065 m/s².
Acceleration of the vehicle
The acceleration of the vehicle is calculated as follows;
v² = u² + 2as
where;
v is the final velocity of the vehicleu is the initial velocity of the vehiclea is the acceleration of the vehicles is the distance traveled by the vehiclev² = 0 + 2as
a = v²/2s
a = (18.84²) / (2 x 29.26)
a = 6.065 m/s²
Thus, the acceleration of the vehicle is 6.065 m/s².
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In which year did Canadian women win the right to vote in elections?
Canadian women won the right to vote in federal elections in the year 1918.
This was a significant moment in Canadian history as it marked a turning point in the fight for women's suffrage. Prior to this, women were not allowed to vote or participate in the political process. However, with the passing of the Canadian Elections Act, women over the age of 21 who were British subjects or wives of British subjects were granted the right to vote. This was a major victory for the suffragette movement in Canada and paved the way for greater gender equality in the country. Today, women's participation in elections and politics is encouraged and celebrated, and the right to vote is seen as a fundamental aspect of democratic societies.
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A 0.42 kg soccer ball is moving down field with a velocity of 12 m/s. A player kicks the ball so that it has a final velocity of 18 m/s down field. What is the change in the balls momentum? and find the constant force exerted by the players foot on the ball if the two are in contact for 0.020 s?
Answer:
the change in momentum is 2.52 N·s
the constant force on the ball while in contact with the players foot is 126 N
Explanation:
p=momentum
m=mass
v=change in velocity
p=(0.42)(6)
p=2.52
The change in the ball's momentum is 2.52 kgms⁻¹
The constant force exerted by the players foot on the ball is 126 N
From the question,
We are to determine the change in momentum of the ball
Change in momentum calculated by using the formula,
\(\rho = m(v-u)\)
Where \(\rho\) is the change in momentum
\(m\) is the mass
\(v\) is the final velocity
and \(u\) is the initial velocity
From the given information,
\(m = 0.42 \ kg\)
\(u = 12 \ m/s\)
\(v = 18 \ m/s\)
Therefore,
Change in the ball's momentum,
\(\rho = 0.42 (18-12)\)
\(\rho = 0.42 (6)\)
\(\rho = 2.52 \ kgms^{-1}\)
Hence, the change in the ball's momentum is 2.52 kgms⁻¹
For the force exerted by the players foot
Force is given by change in momentum with time
That is,
\(F = \frac{\rho}{t}\)
Where
\(F\) is the force
\(\rho\) is the change in momentum
and \(t\) is the time
From the given information
\(t = 0.020 \ s\)
Therefore,
\(F = \frac{2.52}{0.020}\)
\(F = 126 \ N\)
Hence, the constant force exerted by the players foot on the ball is 126 N
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An important underlying feature of hydraulic devices is the conservation of A) pressure.
B) energy
C) momentum.
D) all of the above
E) none of the above
B) energy. An important underlying feature of hydraulic devices is the conservation of energy.
This is achieved through the transfer of energy from one point to another using a pressurized fluid, usually oil or water. The fluid is used to transmit force, and the conservation of energy ensures that the force applied at one end of the system is transferred to the other end without any loss of energy. This makes hydraulic devices highly efficient and effective for a wide range of applications, from construction machinery to aerospace engineering. Liquid fluid power is used by hydraulic machines to do operations. Heavy-duty construction vehicles are a typical illustration. Hydraulic fluid is pumped to numerous hydraulic motors and hydraulic cylinders located all around the machine in this type of machine and is pressurised in accordance with the resistance present.
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Light from an infinite distance way hits a convex lens. Where will the image form?
A.An infinite distance away
B.At the focal point of the lens
C.No image will form
D.Halfway between the focal point and the lens
If light from an infinite distance away hits a convex lens, the image will form at the focal point of the lens. So, the answer is B.
This is because when the object is at an infinite distance, the incoming light rays are parallel to each other. When these parallel rays pass through the convex lens, they converge to a point, which is the focal point of the lens.
Since the light rays converge at the focal point after passing through the lens, the image of the object will be formed at the focal point as well. Therefore, the correct option is B: at the focal point of the lens.
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What is the astronomical unit used to measure distances in the solar system?
Answer:
Astronomical unit
Explanation:
Short Answer: It's (au)
Long Answer:
The astronomical unit (au or AU) is defined as exactly 149,597,870,700 meters (about 93 million mi), which is roughly equal to the average distance between the Sun and Earth.
A car accelerates from 0 m/s to 20 m/s in 5 seconds,
what is the acceleration of the car in m/s2?
Answer:
4
Explanation:
20-0=20 m/s
20/5=4 m/s2
The intensity of the distributed lood acting on the beams 25 kN/m.) Determine the magnitude of reaction at Express your answer to three significant figures and include the appropriate units O ? N Value Units Submit Request Answer Figure Part 6 1 of 1 Delane te zand y components of reaction all sing scalar notation Express your answers using three significant figures separated by a comma HV AED vec ?
The magnitude of reaction at the beam due to the distributed load of 25 kN/m is 625 N.
What is the magnitude of reaction to the distributed load?The magnitude of reaction at the beam can be determined by calculating the total force exerted by the distributed load. In this case, the distributed load is given as 25 kN/m. To find the magnitude of reaction, we multiply the distributed load by the length of the beam.
Therefore, the magnitude of reaction is 25 kN/m multiplied by the length of the beam in meters. By performing the calculation, we obtain the value of 625 N as the magnitude of reaction at the beam due to the distributed load. This represents the total force exerted by the distributed load on the beam.
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ACTIVITY 4
Applying the equation learned, answer the following problems:
1. A bowling ball whose mass is 4.0 kg is rolling at a rate of 2.5 m/s. What is its momentum? p = m/s. What Is Its Momentum?
Given:
Find:
Formula:
Solution:
2. A skateboard is rolling at a velocity of 3.0 m/s with a momentum of 6.0 kg-m/s. What is its mass?
Given:
Find:
Formula:
Solution:
3. A pitcher throws a baseball with a mass of 0.5 kg and a momentum of 10 kg-m/s. What is its velocity?
Given:
Find:
Formula:
Solution:
Subject Is Science
Good Perfect Complete=Brainlist
Copy Wrong Incomplete=Report
Good Luck Answer Brainly Users:-)
Answer:
1) 10 kg-m/s
2) 2 kg
3) 20 m/s
Explanation:
The momentum of an object can be calculated using the equation:
\(\large\boxed{p=mv}\)
where:
p is momentum (measured in kilogram meters per second).m is mass (measured in kilograms).v is the velocity (measured in meters per second).\(\hrulefill\)
Question 1For this question we need to find the momentum of a bowling ball whose mass is 4.0 kg is rolling at a rate of 2.5 m/s.
Given values:
m = 4.0 kgv = 2.5 m/sSubstitute the given values into the momentum formula and solve for p:
\(p=4.0\;\text{kg} \cdot 2.5\;\text{m/s}\)
\(p=10\;\text{kg m/s}\)
Therefore, the momentum of the bowling ball is 10 kg-m/s.
\(\hrulefill\)
Question 2For this question we need to find the mass of a skateboard rolling at a velocity of 3.0 m/s with a momentum of 6.0 kg-m/s.
Given values:
p = 6.0 kg-m/sv = 3.0 m/sAs we want to find mass, rearrange the momentum formula to isolate m:
\(\large\boxed{m=\dfrac{p}{v}}\)
Substitute the given values into the formula and solve for m:
\(m=\dfrac{6.0\; \text{kg m/s}}{3.0\; \text{m/s}}\)
\(m=2\;\text{kg}\)
Therefore, the mass of the skateboard is 2 kg.
\(\hrulefill\)
Question 3For this question we need to find the velocity of a baseball with a mass of 0.5 kg and a momentum of 10 kg-m/s.
Given values:
p = 10 kg-m/sm = 0.5 kgAs we want to find velocity, rearrange the momentum formula to isolate v:
\(\large\boxed{v=\dfrac{p}{m}}\)
Substitute the given values into the formula and solve for v:
\(v=\dfrac{10\; \text{kg m/s}}{0.5\; \text{kg}}\)
\(v=20\;\text{m/s}\)
Therefore, the velocity of the baseball is 20 m/s.
(b) By adding another component to the circuit, the student is able to obtain a range of
ammeter and voltmeter readings.
Ammeter
(amps)
0.10
0.15
0.20
0.25
0.30
Voltmeter
(volts)
1.0
2.0
4.0
7.0
11.0
Question:Which component did the student add to the circuit?
The students add a variable resistor to the circuit
What is a variable resistor?variable resistor is a resistor of which the electric resistance value can be adjusted. A variable resistor is in essence an electro-mechanical transducer and normally works by sliding a contact (wiper) over a resistive element.
A variable resistor gives resistance. Resistance is the opposition to electric current and it is measured in ohms.
From ohm's in law, the potential difference between the ends of a conductor is proportional to current, provided temperature and other physical conditions are kept constant.
This means that by varying the resistor, different values of current and voltages will be acquired.
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A small bar magnet pulls on a larger one with a force of 79 Newtons.
What is the magnitude of the force the larger one exerts on the smaller one?
Answer in units of N.
Answer:
79 N ( the same)
Explanation:
100 points,
The National Park Service sometimes creates controlled burns to mitigate wildfires. How does a controlled burn limit the spread of wildfires?(1 point)
A controlled burn is used to make a path that helps a spreading wildfire arrive at a source of water.
A controlled burn temporarily shuts down parks so people won’t start campfires.
A controlled burn helps to remove plants and vegetation around buildings so a wildfire won’t destroy them.
A controlled burn removes dead vegetation that might otherwise help a wildfire start and spread.
A controlled burn removes dead vegetation that might otherwise help a wildfire start and spread.
What is a controlled burns?The term controlled burn refers to setting up an area in which the fire is controlled in order to avoid wild fires. These are deliberately set up in order to avoid the bush from burning down.
Let us recall that a wild fire is able to blaze across a large causing damage to a buildings as well as life and other properties in the way of the fire and could cause huge looses including loss of habitat.
Thus, the National Park Service sometimes creates controlled burns to mitigate wildfires because a controlled burn removes dead vegetation that might otherwise help a wildfire start and spread.
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When The Syringe Volume Is Suddenly Cut In Half, The Pressure Changes By More Than A Factor Of 2. Why Does It Momentarily Spike Above 200 KPa?
When the syringe volume is suddenly cut in half, the pressure inside the syringe momentarily spikes above 200 kPa due to the compression of the gas inside the syringe.
The pressure is directly proportional to the volume of the gas and inversely proportional to its temperature. When the volume is suddenly reduced, the gas molecules are compressed and collide with each other, increasing the temperature and thus increasing the pressure. This sudden increase in pressure is known as the adiabatic compression.
Additionally, the sudden change in volume also causes turbulence within the syringe, leading to a further increase in pressure. This momentary spike in pressure can have potential consequences such as causing damage to delicate instruments or injuring the operator. Therefore, it is important to handle syringes with care and to be aware of the potential risks associated with sudden changes in volume.
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The relative densities of gold, silver, copper and zinc are given as 19.3, 10.5, 8.9 and 7.1 respectively. A piccc of ornamental metal weighs 0.445 kg and dis- places 5 x 103 m³ when completely immersed in water. The metal is A. zinc B. copper C. silver D. gold
The density of the ornamental metal is closest to the density of copper. The answer is (B) copper
What is the metal?
The density of a substance is given by the mass of the substance divided by its volume:
density = mass / volume
We can use this formula to determine the density of the ornamental metal:
density = mass / volume = 0.445 kg / 5 x 10^3 m^3 = 8.9 x 10^-5 kg/m^3
Next, we can compare this density to the relative densities of gold, silver, copper, and zinc to identify the metal:
Gold: density = 19.3 x 10^3 kg/m^3
Silver: density = 10.5 x 10^3 kg/m^3
Copper: density = 8.9 x 10^3 kg/m^3
Zinc: density = 7.1 x 10^3 kg/m^3
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What is the net force acting on the airplane?
740 N right -->
700 N right -->
100 N left <--
760 N right -->
\(\huge{ \mathrm{ \underline{ Answer }\: \: ✓ }}\)
Total force acting on right side = 800 N
Total force acting on left side :
60 N + 40 N100 NNow, equivalent force acting on the plane is :
greater force - minor force 800 N - 100 N 700 NewtonsAnd the direction of equivalent force will be the direction of greater force, that is right direction.
Hence, Correct option is :
700 N right -->_____________________________
\(\mathrm{ \:TeeNForeveR\:}\)
Which does not represent a change in velocity?
Group of answer choices
A person is riding a bicycle at 4 m/s west and decreases her speed to 3 m/s.
A plane is flying south at 600 km/h and then flies directly upwards before returning to the airport.
A balloon is floating up into the air at 1 m/s.
A bus is traveling west at 2 m/s and then turns a corner.
Answer:
A balloon is floating up into the air at 1 m/s.
Explanation:
Velocity is the displacement divided by the time;
Velocity = \(\frac{displacement}{time}\)
It is a vector quantity that has magnitude and direction.
The choice that shows a change in direction is a correct specification of velocity.
A balloon floating up into the air at 1m/s shows no directional change.
The kicker now kicks the ball with the same speed as in the number of 4,but at 60.0°from the horizontal or 30.0° from the vertical. a.What is the time the ball is in the air? b.What is the distance the balls travel before it hits the ground? c.What is the maximum height?
Answer:
Explanation:
1) The time of flight equation for projectile motion can be used here to find total time in air.
t = 2vsin∅ / g
where v is speed, Ф is launch angle
t = 2×4×sin 60 / 9.8
t = 0.71 seconds
2) Distance where it hit the ground is called as range and has the following standard equation
D = v² sin2Ф/g
D = 4²sin 2×60 / 9.8
D = 1.41m
3) Maximum elevation is maximum time reached
h = v² sin²Ф / 2g
h = 4²sin² 60 / 2*9.8
h = 0.61 m
How to integrate 1/ 1 + x2
The integral of 1/(1 + x²) is (1/2)ln|1 + x²| + C where C is the constant of integration.
Integration is a mathematical process of finding the antiderivative of a function. To integrate the given expression 1/(1 + x²), we will use the substitution method.
Let u = 1 + x², du/dx = 2x dx, then dx = du/2x and the integral becomes:
∫1/(1 + x²) dx = ∫1/u * (1/2x) du= (1/2)∫1/u du
The antiderivative of 1/u is ln|u| + C, where C is the constant of integration.
Therefore, the final solution of the integral is (1/2)ln|1 + x²| + C.
Let us work through the steps:
Step 1:Let u = 1 + x² and then differentiate both sides with respect to x to obtain du/dx. du/dx = 2x
Substitute 2x dx = du into the integral ∫1/(1 + x²) dx to get the integral in terms of u:∫1/u * (1/2x) du = (1/2) ∫1/u du
Step 2:Calculate the antiderivative of 1/u, which is ln|u|. Thus, the final solution is (1/2)ln|1 + x²| + C, where C is the constant of integration. The constant C will vary depending on the initial conditions of the problem.
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#SPJ8
A sloth moves 3 m to the right and then climbs 4 m up a tree.
How many degrees above the ground is the sloth compared to its initial position?
Answer:
The answer is 53.13
Explanation:
Cuz it is. It's not that hard
Answer:
A sloth moves 3 M to the right and then climbs 4 m up a tree.
How many degrees above the ground is the sloth compared to its initial position?
Answer: 53.1°
argue on this can the speed of light be compared to the exact speed if electricity
Answer:
XD
Explanation:
XV