A tennis ball is released from a height h and after freely falling on a wooden floor, it rebounds and reaches height $\frac{h}{2}$. The velocity versus height of the ball during its motion may be represented graphically by: (graphs are drawn schematically and not to the scale) Option: 1 Option: 2 Option: 3 Option: 4

Velocity at the ground (means zero height) is non-zero therefore the option 4 is incorrect.

The velocity versus height curve will be parabolic as for motion under gravity.

i.e The velocity versus height curve is non-linear therefore option 1 is also incorrect.

$\begin{array}{l} \mathrm{v}^{2}=2 \mathrm{gh} \\ \\ \mathrm{v} \frac{\mathrm{dv}}{\mathrm{dh}}=2 \mathrm{~g}=\mathrm{const} \\ \\\Rightarrow \frac{\mathrm{dv}}{\mathrm{dh}}=\frac{\text { constant }}{\mathrm{v}} \end{array}$

Here we can see the slope is very high when velocity is low therefore at the maximum height the slope should be very large which is in option 3 and as velocity increases slope must decrease therefore option 3 is correct.

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