Final answer:
The question asks to calculate the magnitude and direction of the average force exerted by a baseball bat on a baseball after a collision. The calculation involves converting the baseball's initial and final velocities to meters per second, determining the change in momentum, and then using the change in momentum and the time of contact to calculate the average force, which is directed in the +x-direction.
Step-by-step explanation:
To find the magnitude and direction of the average force exerted by the bat on the baseball, we first need to calculate the change in velocity of the baseball and then use this to find the change in momentum. The initial velocity of the baseball is 80 mi/h in the -x-direction, which must be converted to meters per second (m/s). Similarly, the final velocity is 80 mi/h in the +x-direction. The conversion factor is as follows: 1 mi/h = 0.44704 m/s. Once we have the velocities in m/s, the change in momentum (Δp) is equal to the final momentum minus the initial momentum.
Using the formula Δp = m * Δv (where m is the mass and Δv is the change in velocity), we can calculate Δp. The average force (F) can then be found using the equation F = Δp / Δt (where Δt is the time for which the force is applied). Since the Δt given is 20 ms, or 0.020 seconds, we can use this to find the average force.
After performing the necessary calculations, we find the magnitude of the average force and indicate that the direction is in the +x-direction because the baseball was reversed from its initial direction due to the force of the bat.