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Problem:

A ball of mass 0.15 kg is moving with a velocity of 12 m/s and is hit by a bat so that the ball is turned back in the complete opposite direction with a velocity of 20 m/s. The force of the blow acts for 0.01 s on the ball. Find the average force exerted by the bat on the ball.

My attempt:

$$v=u+at$$

$$-20=12+a(0.01)$$

$$a=-3200ms^{-2}$$

$$F=ma$$

$$F=0.15\cdot(-3200)$$

$$F=-480N\text{(Ans.)}$$

My book's attempt:

$$v=u+at$$

$$20=-12+a(0.01)$$

$$a=3200ms^{-2}$$

$$F=ma$$

$$F=0.15\cdot3200$$

$$F=480N\text{(Ans.)}$$

My comments:

I assumed the direction of the initial velocity of the ball to be positive (12 m/s), and the direction of the final velocity of the ball to be negative (-20 m/s). My book did the opposite. They assumed the direction of the initial velocity of the ball to be negative (-12 m/s), and the direction of the final velocity of the ball to be positive (20 m/s). I think that both the solutions are acceptable, but I'm not sure.

My question:

  1. Is my attempt also an acceptable solution to the problem?
tryingtobeastoic
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    I believe both the solutions are acceptable as both are saying the same thing : $480N$ in the given direction. –  May 15 '22 at 06:35
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    Yes, both are fine logically, but just FYI, as currently written, neither is a 'good' way of formally presenting a solution, because physics (also math) is not just about formulas and numbers. You need to define the variables (sign conventions), explain the equations etc while writing up a solution, and state any assumptions you're making along the way (such as assuming the acceleration is constant over that $0.01$s time frame etc), and finally explain what the resulting numbers mean. – peek-a-boo May 15 '22 at 06:45
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    Further to peekaboo's point, my last paragaph here and third point here are examples where the positive direction is carefully specified. – ryang May 15 '22 at 14:43

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