What is the minimum kinetic energy..?

Question

A diagram shows a moving 5.00-kilogram cart at the foot of a hill 10.0 meters high. What is the minimum kinetic energy needed for the cart to move from its current position to reach the top of the hill?

Answer 1

The kinetic energy must be at least equal to the potential energy at the top of the hill, by energy conservation.  For minimum kinetic energy (KE),

 

KE = potential energy at top = mgh = (5 kg)(9.8 m/s^2)(10 m) = 490 J