In our simple model of the fight of a ball, the height

y above the foor at time t is

$\displaystyle y = V_{n}t-\frac{1}{2}gt^{2} $

where g is the acceleration due to gravity and vn is the velocity immediately after the nth bounce.

The maximum height of the ball is reached when dy/dt = 0

Find the time

tmax at which this maximum occurs and the maximum height

ymax that the ball reaches.

I am really not sure how to do this, since I do not know what vn is?

$\displaystyle \frac{dy}{dt} = V_{n} -gt = 0 $

$\displaystyle V_{n} = gt $

dont know how to work ourt $\displaystyle y_{max} $

and $\displaystyle t_{max} $