Question

A ball is dropped vertically from a height d above the ground. It hits the ground and bounces up vertically to a height d/2. neglecting subsequent motion and air resistance, its velocity v varies with height h above the ground as

Answer 1

The graph (in 1st pic) between h and v will be a parabola. At h=dh=d , velocity is zero,

( Taking downward direction as negative)

Then its negetive value increases , and at h=0h=0 velocity gets reversed and then goes on decreasing and becomes zero at h=d/2

or

at height H above the ground for downward motion,
v = √2g(d-h)
also,
$\frac{vdv}{dh} = - g \: \: \: \: \: \: \: \: \: \: or \: \: \: \: \: \: \: \: \: \: \frac{dv}{dh} = \frac{g}{v}$
the graph is rising and increasing because greater than smaller is v, at height h above the ground for upward motion,
v = √2g(d/2-h)


also,
vdv/dh= -g. or. dv/dh = g/v
the graph is falling and increasing because greater the h smaller is v
the graph is drawn in second pic