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  4. A particle of mass m is projected with velocity v making an angle of 45° with the horizontal. When the particle lands on the level ground the magnitude of the change in its momentum will be

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Q. A particle of mass m is projected with velocity v making an angle of $45^\circ$ with the horizontal. When the particle lands on the level ground the magnitude of the change in its momentum will be

AIPMTAIPMT 2008Motion in a Plane

Solution:

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The horizontal momentum does not change. The change in vertical momentum is
$m v \sin \theta-(-m v \sin \theta)=2 m v \frac{1}{\sqrt{2}}=\sqrt{2}\, m v$