Question

An object of m kg with speed vm/s strikes a wall at an angle a and rebounds at the same speed and same angle.find the magnitude of change in the momentum of object.

Answer 1

see figure, it is clearly shown that an object of mass m kg with speed v m/s strikes a wall at an angle α and rebounds at the same speed and same angle.

so, velocity of particle just before striking the wall, $u_i=vsin\alpha\hat{i}-vcos\alpha\hat{j}$

so, initial momentum of particle, Pi = $mv(sin\alpha\hat{i}-cos\alpha\hat{j})$

velocity of particle just after striking the wall, $u_f=-vsin\alpha\hat{i}-vcos\alpha\hat{j}$

so, final momentum of particle, Pf = $mv(-sin\alpha\hat{i}-cos\alpha\hat{j})$

now , change in momentum = Pf - Pi

= $mv(-sin\alpha\hat{i}-cos\alpha\hat{j}-mv(sin\alpha\hat{i}-cos\alpha\hat{j})$

= $-2mvsin\alpha\hat{i}$

hence, magnitude of change of momentum = 2mvsinα