In a Little League baseball game, the 145 g ball enters the strike zone with a speed of 15.0 m/s . The batter hits the ball, and it leaves his bat with a speed of 21.0 m/s in exactly the opposite direction. What is the magnitude of the impulse delivered by the bat to the ball?

5.22 Ns

Explanation:

A consequence of Newton's second law of motion is that:

Impulse = change in momentum

The initial momentum = (0.145 kg) × (15.0 m/s)

The final momentum = (0.145 kg) × (-21.0 m/s)

The final momentum has a negative sign because the ball returned in an opposite direction.

Change in momentum = final momentum - initial momentum = (0.145 kg) × (-21.0 m/s) - (0.145 kg) × (15.0 m/s)

= -0.145(21.0 + 15.0) kg m/s

= -0.145 × 36.0 kg m/s

= -5.22 kg m/s

The magnitude of the impulse is thus 5.22 Ns.

force required to detach it is given by

charges are taken to be fundamental charge

now we have

so above is the minimum distance at which it will detach