Question

A ball of mass 'm' is projected from the ground with a speed 'u' at an angle ' $\alpha$' with the horizontal. The magnitude of the change in momentum of the ball over a time interval from begining till it strikes the ground again is

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

Answer 1

Answer: (D)

$2mu\sin \alpha$

Over the course of the journey, the velocity of the ball in the x-direction is constant. So the momentum in that direction remains the same.
Initial momentum in y-direction $p_{yi}=musin\alpha$
Final momentum in y-direction $p_{yf}=-musin\alpha$
$\therefore$ change in momentum $=-2musin\alpha$
Magnitude of change $=2musin\alpha$