A ball of mass m hits a floor with a speed v making an angle of incidence theta with the normal. The coefficient of restitution is .e.. Find the speed of the reflected ball and the angle of reflection of the ball.

A ball of mass m hits a floor with a speed v making an angle of incide

1.	A ball of mass m hits a floor with a speed v making an angle of incidence theta with the normal. The coefficient of restitution is .e.. Find the speed of the reflected ball and the angle of reflection of the ball.
Answer» Solution :Suppose the angle of reflection is `theta.` and the speed after the COLLISION is v.. The floor exerts a force on the BALL ALONG the normal during the collision. There is no force parallel to the surface. Thus, the parallel component of the velocity of the ball remains unchanged. This gives v. in `theta .` = v sin `theta ""` ......(i) For the components normal to the floor, the velocity of separation is v. cos `theta.` and the velocity of APPROACH is v cos `theta`. Hence, v. cos `theta.` = EV cos `theta ""` .....(ii) From (i) and (ii), `v. = v sqrt(sin^(2)theta+e^(2)cos^(2)theta)` and `tan theta. = (tan theta)/(e ) rArr e = (tan theta)/(tan theta^(1))`