Answer:
3 m
Step-by-step explanation:
You want to know the height at which a rock dropped from a height of 9 m has twice as much kinetic energy as potential energy.
Ratio
The ratio of KE to PE is given as ...
KE : PE = 2 : 1
This means the potential energy of the rock is 1/(2+1) = 1/3 of the total energy the rock has.
Potential energy
When the rock is dropped, all of its energy is potential energy. As the rock falls, that potential energy is converted to kinetic energy. The remaining potential energy is proportional to the height of the rock.
If the remaining potential energy is 1/3 of the original potential energy, the height of the rock is 1/3 the original height:
(1/3)×(9 m) = 3 m
When the rock is 3 m high, the kinetic energy is twice the potential energy.