Final answer:
The average force exerted by the bat on the baseball is 4900 N in the direction of the pitcher, calculated by determining the change in momentum (9.8 kg*m/s) and dividing it by the time interval (0.002 s).
Step-by-step explanation:
To calculate the average force exerted by the bat on the baseball, we need to find the change in momentum (impulse) and divide it by the time interval during which the force is applied. The ball's momentum changes from moving at 30.0 m/s in one direction to 40.0 m/s in the opposite direction. Therefore, the total change in velocity is 70.0 m/s.
The change in momentum is given by Δp = m * Δv, where 'm' is the mass of the baseball (0.140 kg) and 'Δv' is the change in velocity (70.0 m/s). Therefore, the change in momentum is 0.140 kg * 70.0 m/s = 9.8 kg*m/s.
The average force (F) exerted by the bat can then be calculated using the formula F = Δp / Δt, where Δp is the change in momentum and Δt is the time interval (2.0 ms or 0.002 s). We then get F = 9.8 kg*m/s / 0.002 s = 4900 N.
Thus, the average force exerted by the bat on the baseball is 4900 N in the direction of the pitcher.