Alejandro Kirk is the catcher for the Blue Jays’ baseball team. He exerts a forward force on the 0.145-kg baseball to bring it to rest from a speed of 38.2 m/s. During the process, his hand recoils a distance of 0.135 m. Determine is the acceleration of the ball.
Determine the force applied by Alejandro.

a= -5404.6 [m/s²]; F=785.75 [N].

Explanation:

1. Determine is the acceleration of the ball:

equation of the distance (0.135m) is:

 where S=0.135[m]; a - required acceleration; t - elapsed time; v₀ - initial velocity (38.2 m/s);

also the required acceleration is:

V - the end velocity (0 m/s), t - elapsed time, ₀ - initial velocity (38.2 m/s).

Using the equations of reqruired acceleration and the distance it is possible to make up and solve the next system:

finally, a≈-5404.6 [m/s²].

2. Determine the force applied by Alejandro.

the energy is:

According to these two equations, the required force is:

F=0.145*38.8²/2/0.135≈785.75 [N].

note, the suggested way is not the shortest one and not the only one.

P.S. if it is possible, check the arithmetic operations and the provided answers in other sources.

it is a negative acceleration