A wedge can slide frictionlessly on a fixed incline of angle 37°. A girl who is strapped on the wedge [no relative motion between wedge and girl] pushes a small ball of negligible mass on the horizont

Question

A wedge can slide frictionlessly on a fixed incline of angle 37°. A girl who is strapped on the wedge [no relative motion between wedge and girl] pushes a small ball of negligible mass on the horizontal smooth upper surface of wedge as shown in figure. Ball is pushed at the same instant as the motion of wedge starts. Initial velocity of ball is 24 m/s relative to wedge. Find the time (in sec) after which ball returns to girl. Assume that horizontal surface of wedge is very long.

TestHub · Accepted Answer

The wedge slides down with acceleration $g sin θ$ ; relative to the wedge, the ball's acceleration along the surface is $- g sin θ cos θ$

The ball returns when its relative displacement is zero: $0 = u t - \frac{1}{2} g sin θ cos θ t^{2}$

$t = \frac{2 u}{g s i n θ c o s θ} = \frac{2 \times 24}{10 \times 0.6 \times 0.8} = 10$ s

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