I've done part (a) but cannot understand the method of how part (b) is done. I've written down the answer I obtained (which is correct) to part (a). Can someone help? Thanks in advance.

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Q:

A small smooth ball of mass is moving on a horizontal table with speed when it collides directly with another small smooth ball of mass which is at rest on the table. The balls have the same radius and the coefficient of restitution between the balls is . The direction of motion of is reversed as a result of the collision.

(a) Find, in terms of and . the speeds of and immediately after the collision.

In the subsequent motion strikes a vertical wall, which is perpendicular to the direction of motion of , and rebounds. The coefficient of restitution between and the wall is .

Given that there is a second collision between and ,

(b) find the range of values of for which the motion described is possible.

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A:

(a)