When will they collide?

Classical Mechanics Level 3

At \( t = 0\) , 2 balls \(b_{1}\) and \(b_{2}\) are dropped from rest from heights of \(10 m\) and \(40 m\) respectively.

Also at \( t = 0\) , a very large heavy plank starts to move upward with speed \(5~m/s\).

Find the time \(T\) (in sec) at which the balls collide for the first time.

\( \textbf{NOTE-}\)

Motion takes place in vertical plane

\( g = 10 ~m/s^{2}\)

Assume all collisions as \(elastic\).

The plank still moves with speed \( 5~m/s\) after collision with the ball \(b_{1}\)

The mass of the balls are negligible as compared to that of the plank.

The balls are to be considered point objects.

Collision takes negligible time


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