Question

A ball of mass ${}^{\prime }{m}^{\prime }$ is projected from the ground with a speed ${}^{\prime }{u}^{\prime }$ at an angle ' $\alpha$' with the horizontal. The magnitude of the change in momentum of the ball over a time interval in which it reaches the maximum height is :

• A. $mu\sin \alpha$
• B. $2mu\cos \alpha$
• C. $\frac{mu\cos \alpha }{2}$
• D. $2mu\sin \alpha$

Answer 1

The correct option is A $mu\sin \alpha$

The velocity of the ball along the x-direction does not change
$\therefore △v_x=0\Rightarrow △p_x=0$
Initial velocity along y-direction$=usin\alpha \Rightarrow p_{y_{initial}}=musin\alpha \hat{j}$
Velocity along y-direction at topmost point $=0\Rightarrow p_{y_{final}}=0$
$\therefore △p_y=-musin\alpha \hat{j}$
$\therefore △p=△p_x+△p_y=-musin\alpha \hat{j}$
$\Rightarrow$ Change in magnitude of momentum $=musin\alpha$