question_answer

A projectile is projected with a linear momentum p making an angle 9 with the horizontal. The change in momentum of the projectile on return to the ground will be

A)  \[2\,p\tan \theta \]

B)  \[2\,p\sin \theta \]

C)  \[2\,p\cos \theta \]

D)  2p

Correct Answer: B

Solution :

\[\left| ({{P}_{f}}-{{P}_{i}} \right|=\] Change in momentum \[=\sqrt{{{P}^{2}}+{{P}^{2}}+2P\,.\,P\cos \,\,(\pi -2\theta )}\] \[=P\sqrt{2+2(-\cos \theta )}\] \[=P\sqrt{2\,\,(2{{\sin }^{2}}\theta )}\] \[=2P\,\,\sin \,\,\theta \]