A ball is released from position A and travels 5m before striking the smooth fixed inclined plane as shown. If the coefficient of restitution in the impact is e = \frac{1}{2}, the time taken by the ball to strike the plane again is

Engineering

Physics

Motion of Block on Inclined Surface

Collision

Projectile Motion

Question

A ball is released from position A and travels 5m before striking the smooth fixed inclined plane as shown. If the coefficient of restitution in the impact is $e = \frac{1}{2}$ , the time taken by the ball to strike the plane again is

2.5s

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Just before first collision,
speed $u = \sqrt{2 g (5)} = 10 m / s$

$u_{y} = - 10 \cos 30 ° = - 5 \sqrt{3}$

u_x = 10 sin 30° = 5 m/s
v_x = u_x = 5 m/s

$v_{y} = - {eu}_{y} = \frac{5}{2} \sqrt{3}$

It strikes the plane again at time,

$t = \frac{2 vy}{gcos 30 °} = 1 \sec$ .