A rock falls from a vertical cliff that is 4.0 m tall and experiences no significant air resistance as it falls.At what speed will its gravitational potential energy (relative to the base of the cliff)be equal to its kinetic energy?
A)3.1 m/s
B)4.4 m/s
C)6.3 m/s
D)8.9 m/s
E)13 m/s

Question

Quizplus · Accepted Answer

The gravitational potential energy of the rock at the top of the cliff is given by:
PE = mgh
where m = mass of the rock, g = acceleration due to gravity, and h = height of the cliff.
At the base of the cliff, all the potential energy is converted into kinetic energy, given by:
KE = (1/2)mv^2
where v = speed of the rock.
At the point where PE = KE, we have:
mgh = (1/2)mv^2
Simplifying, we get:
v = sqrt(2gh)
Substituting the given values, we get:
v = sqrt(2 x 9.81 x 4.0) = 6.3 m/s
Therefore, the correct answer is C) 6.3 m/s.

A Rock Falls from a Vertical Cliff That Is 4