Question

A 1,200 kg car rolls down a hill with its brakes off and transmission in neutral. At one moment it is moving 5.0 m/s. A little later it is moving at 8.2 m/s. How much did its height change between the two times? Assume friction and air resistance have no effect on its motion.

Answer 1

Since its a lossless system we can assume the increase in kinetic energy equals the loss in gravitational potential energy.
(1/2)m(v2^2-v1^2)=mg(delta H)
Divide out mass and solve for delta H, dH:
dH=(v2^2-v1^2)/2g = 2.153m