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  4. 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

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Q. 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

NTA AbhyasNTA Abhyas 2020Motion in a Straight Line

Solution:

(i) For uniformly accelerated/deaccelerated motion, $v^{2}=u^{2}\pm2gh$
i.e., v - h graph will be a parabola (because the equation is quadratic).
(ii) Initially, velocity is downwards (-ve) and then after the collision it reverses its direction with lesser magnitude. i.e., velocity is upwards (+ve). Graph (a) satisfies both these conditions.
Note that time $t=0$ corresponds to the point on the graph where $h=d$ .
Solution