Question

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

• A. $2p\cot \theta$
• B. $2p\sin \theta$
• C. $2p\cos \theta$
• D. Remains unchanged

Answer 1

The correct option is B $2p\sin \theta$

$|(P_t-P_i)|=$Change in momentum
$=\sqrt{P^2+P^2+2P\cdot P\cos (\pi -2\theta )}$
$=P\sqrt{2+2(-\cos 2\theta )}$
$=P\sqrt{2\left(2{\sin }^2\theta \right)}$
$=2P\sin \theta$.