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:
- Is my attempt also an acceptable solution to the problem?