Ball hitting the bat

Classical Mechanics Level 2

A ball approaches a batsman horizontally at speed \(v_{\text{ball}}\), and the batsman swings the bat, hitting the ball back along the same path. If the speed of the bat is \(v_{\text{bat}}\) when it hits the ball, then what is the recoil speed of the ball?

\(\)
Details and Assumptions:

The collision is perfectly elastic.
For all practical purposes, the speed of the bat is constant throughout the collision.

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