Question

A projectile is projected with a linear momentum $p$ making an angle $ \theta $ with the horizontal. The change in momentum of the projectile on return to the ground will be

• A. $ 2p\,\tan\,\theta $
• B. $ 2p\,\sin\,\theta $
• C. $ 2p\,\cos\,\theta $
• D. $ ~2p $

Answer 1

Answer: (B)

$\mid\left( P _{f}- P _{i}\right)=\mid$ Change in momentum

$=\sqrt{P^{2}+P^{2}+2 P \cdot P \cos (\pi-2 \theta)}$
$=P \sqrt{2+2(-\cos \theta)}$
$=P \sqrt{2\left(2 \sin ^{2} \theta\right)}$
$=2 P \sin \theta$