A ball is thrown into a 90° smooth corner with an initial velocity v. Denoting the coefficient of restitution by e,

Engineering

Physics

Newtons Second Law of Motion

Collision

Relative Motion

Question

A ball is thrown into a 90° smooth corner with an initial velocity v. Denoting the coefficient of restitution by e,

The final velocity is of magnitude e²v.

The final velocity after second collision is of magnitude ev.

The angle between initial direction of motion during first collision and final direction of motion after second collision is zero.

The angle between initial direction of motion during first collision and final direction of motion after second collision is 45°.

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$\vec{v} = v_{x} i - v_{y} j$

After the first impact x component is multiplied by e and the y component is unchanged

$\vec{v} = - {ev}_{x} i - v_{y} j$

After rebound at C the y component is multiplied by e and the x component is unchanged

$\vec{v} = - {ev}_{x} i + {ev}_{y} j = - (v_{x} i - v_{y} j)$

So $\vec{v} = - e \vec{v}$ and the final velocity is parallel to the original velocity.