First slide

Collisions

Question

Three identical particle with velocities $v_{0} \hat{i}, - 3 v_{0} \hat{j}$ and $5 v_{0} \hat{k}$ collide successively with each other in such a way that they form a single particle. The velocity vector of resultant particle is

Moderate

A

$\frac{v_{0}}{3} (\hat{i} + \hat{j} + \hat{k})$
B

$\frac{v_{0}}{3} (\hat{i} - \hat{j} + \hat{k})$
C

$\frac{v_{0}}{3} (\hat{i} - 3 \hat{j} + \hat{k})$
D

$\frac{v_{0}}{3} (\hat{i} - 3 \hat{j} + 5 \hat{k})$

Solution

$\begin{array}{l} f r o m p r i n c i p l e o f c o n s e r v a t i o n o f l i n e a r m o m e n t u m \\ {\vec{P}}_{i n i t i a l} = {\vec{P}}_{f i n a l} \\ ∴ m (v_{0} \hat{i}) + m (- 3 v_{0} \hat{j}) + m (5 v_{0} \hat{k}) = 3 m \vec{v} \\ ∴ \vec{v} = \frac{v_{0}}{3} (\hat{i} - 3 \hat{j} + 5 \hat{k}) \end{array}$

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