Initially there is a small ball moving with speed 2v towards wall A and both walls are moving with constant velocity towards each other as shown in figure. Then find speed v (in m/s) if time taken by the ball in first three collision is 5 sec. (Assume all collision are perfectly elastic and friction is absent).

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Each elastic hit on an approaching wall adds $2 v$ to the ball's speed: $2 v \to 4 v \to 6 v$ . Leg 1: closing speed $2 v + v = 3 v, t_{1} = \frac{105}{3 v} = \frac{35}{v}$ ; separation left $= 105 - 2 v t_{1} = 35 m$ . Leg 2: closing $4 v + v = 5 v, t_{2} = \frac{35}{5 v} = \frac{7}{v}$ ; separation left $= 35 - 14 = 21 m$ . Leg 3: closing $6 v + v = 7 v, t_{3} = \frac{21}{7 v} = \frac{3}{v}$ . $\frac{35 + 7 + 3}{v} = 5 \Rightarrow v = 9 m / s$ . Answer: 9

Answer: 9

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