First slide

Collisions

Question

A particle of mass m moving eastward with a speed v collides with another particle of the same mass moving northward with the same speed v. The two particles coalesce on collision. The new particle of mass 2m will move in the north-easterly direction with a velocity

Moderate

A

v/2
B

2v
C

$v / \sqrt{2}$
D

v

Solution

Initial momentum of the system
${\vec{P}}_{i} = mv \hat{i} + mv \hat{j}$
$| {\vec{P}}_{i} | = \sqrt{2} mv$
Final momentum of the system = 2mV
By the law of conservation of momentum
$\sqrt{2} mv = 2 mV \Rightarrow V = \frac{v}{\sqrt{2}}$

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