Question

A ball collides elastically with a massive wall moving towards it with a velocity of $v$ as shown. The collision occurs at a height of h above ground level and the velocity of the ball just before collision is $2v$ in horizontal direction. The distance between the foot of the wall and the point on the ground where the ball lands, at the instant the ball lands, will be.

• A. $v\sqrt{\frac{2h}{g}}$
• B. $2v\sqrt{\frac{2h}{g}}$
• C. $4v\sqrt{\frac{2h}{g}}$
• D. $3v\sqrt{\frac{2h}{g}}$

Answer 1

The correct option is D $3v\sqrt{\frac{2h}{g}}$

$\text{Solve in the reference frame fixed to the wall.}$

$\text{Before collision, velocity of ball}=3v\text{towards it.}$

$\therefore \text{After elastic collision of ball}=3v\text{away from it.}$

$\text{Time of flight}=\sqrt{\frac{2h}{g}}$

$\therefore \text{Distance between wall and ball}=3v\sqrt{\frac{2h}{g}}$