Question:
Two identical balls are moving towards a wall with equal speed. The first ball hits the wall perpendicular to the wall and the second ball hits the game wall at an angle of 60 degrees and gets reflected. Find the ratio of the impulse exerted by the wall on the two balls.
Answer:
Let the angle of incidence of ball 1 onto the wall be=A
Let the angle of incidence of the ball 2 be=B
Let the speed of the balls just before striking the wall =v
The velocity vectors (incident and reflected) are resolved along the normal to the wall and along the wall.
For the change in velocity of ball 1 =vf−vi
=(vcosAj+vsinAi)−(vsinAi−vcosAj)=2vcosAj
Impulse = change in the momentum of ball 1=2mvcosAj
So the direction of force = direction of momentum = normal to the wall, coming out of the wall.
ratio of impulses =(2mvcosA)(2mvCosB)=cosAcosB
= ratio of cosines of angles of incidence.
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