A tennis ball is released from height h above
ground level. If the ball makes inelastic collision
with the gound, to what height will it rise after
third collision
(a) he⁶ (b) e²h
(c) e³h (d) None of these
Answers
Answer:
Given that,
Height = h
Final velocity = v
Initial velocity = u
Coefficient restitution = e
We know that,
Restitution = the square root of the ratio of the kinetic energy before and after collision
$$ e=\dfrac{v}{u}=\sqrt{\dfrac{{{K}_{1}}}{{{K}_{0}}}} $$
$$ {{K}_{1}}={{e}^{2}}{{K}_{0}} $$
$$ {{K}_{2}}={{e}^{2}}{{K}_{1}} $$
$$ {{K}_{2}}={{e}^{4}}{{K}_{0}} $$
Similarly,
$$ {{K}_{3}}={{e}^{4}}{{K}_{2}} $$
$$ {{K}_{3}}={{e}^{6}}{{K}_{0}} $$
We know that,
The kinetic energy is
$$ mgh=K $$
$$ h=\dfrac{K}{mg} $$
The ball is initially dropped from the height hand acquires a kinetic energy K0 when it hits the ground, before the first collision.
mgh=K0
Now, Ifh1, h2and h3 are the heights after the first, second and third collisions
$$ {{h}_{1}}=\dfrac{{{K}_{1}}}{mg}={{e}^{2}}\dfrac{{{K}_{0}}}{mg}={{e}^{2}}h $$
$$ {{h}_{2}}={{e}^{4}}h $$
$$ {{h}_{3}}={{e}^{6}}h $$
Hence, the height raised by the ball after third collision is e6h
Answer:
A tennis ball is released from height h above
ground level. If the ball makes inelastic collision
with the gound, to what height will it rise after
third collision
(a) he⁶
(b) e²h
(c) e³h ✔️✔️
(d) None of these