Question

A 5.0-kg rock is dropped from a height of 21.0 m. At what height is the rock's kinetic energy twice its potential energy? answer:___m

Answer 1

When, the rock is located at the maximum height, there is no kinetic energy and the total mechanical energy is the potential energy:

`E_1=U_1=mgh_(max)`

When the rock is located at a height such that the kinetic energy is twice the potential energy, we have:

`\begin{gathered} E_2=U_2+K_2 \\ \\ =U_2+2U_2 \\ \\ =3U_2 \\ \\ =3mgh \end{gathered}`

Since the mechanical energy is conserved, then:

`\begin{gathered} 3mgh=mgh_(max) \\ \\ \Rightarrow h=(1)/(3)h_(max) \end{gathered}`

Replace h_max=21.0m to find the height at which the kinetic energy of the rock is twice the potential energy of the rock:

`h=(1)/(3)(21.0m)=7.0m`

Therefore, the answer is: 7m.