Question

A 2.0 kilogram ball rolling along a flat surface starts up a hill. If the ball reaches a height of 0.63 meters, what was its initial speed

Answer 1

The potential energy as it reaches a height of 0.63 meters is mgh
Since total mechanical energy is conserved, Set that equal to the initial kinetic energy which is 0.5mv^2

2*9.8*0.63 = 0.5*2*v^2
12.348 = v^2
3.51 = v

That's it's initial speed.