A man of right side jumps right with a speed V relative to the plank at rest. After that left man also jumps left with a relative velocity V with respect to plank's velocity. The final velocity o

Question

A man of right side jumps right with a speed V relative to the plank at rest. After that left man also jumps left with a relative velocity V with respect to plank's velocity. The final velocity of plank will be :

TestHub · Accepted Answer

Take right as positive. Each jump speed V is measured relative to the plank just after that jump.

Let the plank speed after the first jump be u. The right man then has ground speed u + V.

$m (u + V) + 3 m u = 0$

$u = - \frac{V}{4}$

Before the second jump, the remaining man and plank move together at u.

Let their final plank speed be w. The left man has ground speed w - V.

$3 m u = m (w - V) + 2 m w$

$3 (- \frac{V}{4}) = 3 w - V$

$w = \frac{V}{12} right$

Option D.

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