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  4. A Tennis ball is released from a height h and after freely falling on a wooden floor it rebounds and reaches height ( h /2) . The velocity versus height of the ball during its motion may be represented graphically by: (graph are drawn schematically and on not to scale)

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Q. 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 : (graph are drawn schematically and on not to scale)

JEE MainJEE Main 2020Motion in a Straight Line

Solution:

Velocity at ground (means zero height) is nonzero therefore one is incorrect and velocity versus height is non-linear therefore two is also incorrect.
$v ^{2}=2 gh$
$v \frac{ dv }{ dh }=2 g = const.$
$\frac{d v}{d h}=\frac{\text{constant}}{v}$
Here we can see slope is very high when velocity is low therefore at Maximum height the slope should be very large which is in option 3 and as velocity increases slope must decrease there for option 3 is correct.