First slide

Collisions

Question

A particle of mass 4m is projected from the ground at some angle with horizontal. Its horizontal range is R. At the highest point of its path it breaks into two pieces of masses m and 3m, respectively, such that the smaller mass comes to rest. The larger mass finally falls at a distance x from the point of projection, where x is equal to

Moderate

A

$\frac{2 R}{3}$
B

$\frac{7 R}{6}$
C

$\frac{5 R}{4}$
D

none of these

Solution

Apply conservation of momentum at highest point:
$4 mucos θ = 3 mv \Rightarrow v = \frac{4}{3} ucos θ . . . . (i)$
$\begin{array}{l} R = (ucos θ) T \\ R_{1} = v \frac{T}{2} = \frac{4}{3} \frac{ucos θT}{2} = \frac{2 R}{3} \\ \Rightarrow x = \frac{R}{2} + R_{1} = \frac{R}{2} + \frac{2 R}{3} = \frac{7 R}{6} \end{array}$

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