For a falling particle the gravitational acceleration is given by

\overset{\cdot\cdot}{y} = g

where the 'double dot' denotes differentiation with respect to time

t

and

y

is measured vertically downwards. By integrating this equation derive the equations of motion where the velocity at time t is denoted by

v = \overset{\cdot}{y}

and the initial velocity

v (0) = u

. From the equations you have found deduce the energy equation.

Two balls are dropped from rest, one vertically above the other. The lower ball hits the ground and bounces back vertically with the same speed with which it hit the ground (coefficient of restitution 1). From what height does the higher ball have to be dropped in order to hit the lower ball before it starts to fall again after rebounding?