A boulder with a mass of 48.3kg is sitting on the top of a 11.8m tall cliff, and the boulder falls off of the cliff. At what height above the ground is the boulder when it reaches a velocity of 6.40m/s?
I found that the kinetic energy of the boulder before it falls off is 5585.412 Joules.
I also found out that when the boulder reaches the velocity of 6.40m/s, its kinetic energy is 989.184 Joules.
Are these correct so far?
Also, what is the velocity of the boulder as it hits the ground?
velocity at ground:
InitialPE=finalKE
mgh=1/2 m v^2
v=sqrt(2gh)=sqrt(2*9.8*11.8)
notice you wrote initial KE, you meant initial Potential energy. The initial KE is zero (sitting on a cliff)>
To verify if your calculations are correct, we can use the equations for potential energy and kinetic energy.
The potential energy (PE) of an object at height h is given by the formula: PE = mass * gravity * height. We know the mass of the boulder is 48.3kg and the height of the cliff is 11.8m. Assuming gravity is approximately 9.8 m/s², we can calculate the potential energy before the boulder falls:
PE = 48.3kg * 9.8 m/s² * 11.8m
PE = 5612.716 Joules
Therefore, the potential energy of the boulder at the top of the cliff is approximately 5612.716 Joules.
Now, let's confirm if the kinetic energy values you calculated are correct. The kinetic energy (KE) of an object is given by the formula: KE = 0.5 * mass * velocity^2. We know the mass of the boulder is still 48.3kg, and the velocity when it reaches a certain height is 6.40m/s.
KE = 0.5 * 48.3kg * (6.40m/s)^2
KE = 983.872 Joules
Therefore, when the boulder reaches the velocity of 6.40m/s, its kinetic energy should be approximately 983.872 Joules, not 989.184 Joules as you suggested.
To find out at what height above the ground the boulder is when it reaches a velocity of 6.40m/s, we can rearrange the equation for potential energy and solve for height:
PE = KE
mass * gravity * height = 0.5 * mass * velocity^2
Canceling out the mass on both sides of the equation, we get:
gravity * height = 0.5 * velocity^2
Now, we can substitute the known values:
9.8 m/s² * height = 0.5 * (6.40m/s)^2
Simplifying further:
height = (0.5 * (6.40m/s)^2) / (9.8 m/s²)
height = 2.073 meters
Therefore, the boulder is approximately 2.073 meters above the ground when it reaches a velocity of 6.40m/s.
So, to recap: the potential energy at the top of the cliff is approximately 5612.716 Joules, the kinetic energy when the boulder reaches a velocity of 6.40m/s is approximately 983.872 Joules, and the height above the ground at that point is approximately 2.073 meters.