A small ball falling vertically downward with constant velocity 4m/s strikes elastically a massive inclined cart moving with velocity 4 m/s horizontally as shown. Find the velocity of the rebound of the ball (answer in multiple of $\sqrt 5$ m/sec)

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Solution

By law,

when the ball rebounds, it experiences the same amount
of momentum in the opposite direction.

Hence,

change in momentum = $2 \times ρ$

Relative velocity ( ball ) ,

-v along x - axis directed to the right

-v along y - axis directed up

After rebound,

v along x - axis directed to the left

v along y - axis directed down

Therefore,

velocity ( rebounded ball ) = $\sqrt{(} 2 v)^{2} + v^{2}$

$v \sqrt{5}$

velocity ( rebounded ball ) = $4 \sqrt{5}$ m/s

Hence, the velocity of the rebounded ball is $4 \sqrt{5}$ m/s

The answer is (d ) $4 \sqrt{5}$ m/s

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A small ball falling vertically downward with constant velocity 4m/s strikes elastically a massive inclined cart moving with velocity 4 m/s horizontally as shown. Find the velocity of the rebound of the ball (answer in multiple of √5 m/sec)

A small ball falling vertically downward with constant velocity 4m/s strikes elastically a massive inclined cart moving with velocity 4 m/s horizontally as shown. Find the velocity of the rebound of the ball (answer in multiple of $\sqrt 5$ m/sec)