Question

A woman throws a cricket ball upwards into the air. The ball leaves the womans hand at 1.8m above the ground at speed of 9.7. It rises and then falls back to the ground. Considering the energies involved calculate the speed at the point it hits the ground.

accerlation due to gravity (g) is 9.8 m s, neglect air resistance

Answer 1

Equate final kinetic energy to initial kinetic and potential energies.

Initial:
KE=(1/2)m(9.7)²
PE=mg(1.8)

Final:
KE=(1/2)mv²
PE=0

All energies are in joules if you work with metres, kilograms and seconds.

Answer 2

Is that the same as

Ek = ½mv² - ½mu²

or does mgh have to be in the equation?

Answer 3

mgh has to be in the equation because the ball was initially 1.8m higher than the ground. The velocity required is at ground level.
(1/2)mv²=(1/2)mu²+mgh

u,v being initial and final velocities.