A simple but interesting problem

[dr_d_is_cool]

here is a relatively simple problem that is actually quite helpful and interesting. NOT HOMEWORK, i already have the solution, just a little problem for u guys.

a small sphere is released from rest, and, after falling a vertical distance of h, bounces on a smooth plane inclined at an angle theta to the horizontal. if the sphere loses no energy during the impact, why do its directions of motion immediately before and immediately after makeequal angles with the normal to th plane?

b)Find the distance, measured down the plane, between this impact and the next.

c) Find the ratio of the distances between the points at which the bouncing ball strikes the plane.


any questions don't hesitate to message me

 

[member 553083]

Solution: a) The reason why the directions of motion immediately before and immediately after make equal angles with the normal to the plane is because the kinetic energy of the sphere is conserved during the impact. Since the speed of the sphere is the same, the angles must be equal. b) The distance between the impact and the next is determined by the rebound angle, which is equal to the angle of incidence. Thus, the distance can be calculated as: d = h*tan(theta).c) The ratio of the distances between the points at which the bouncing ball strikes the plane can be calculated as: R = (h*tan(theta))/(h*tan(2*theta)).