Question

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.

Answer 1

a= -5404.6 [m/s²]; F=785.75 [N].

Step-by-step explanation:

1. Determine is the acceleration of the ball:

equation of the distance (0.135m) is:

`S=-(at^2)/(2) +v_0t,` where S=0.135[m]; a - required acceleration; t - elapsed time; v₀ - initial velocity (38.2 m/s);

also the required acceleration is:

`a=(v-v_0)/(t), where` 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:

`\left \{ {{a=-(38.2)/(t) } \atop {S=-(at^2)/(2)+38.2t }} \right. \ => \ \left \{ {{a=-(38.2)/(t) } \atop {0.5at^2-38.2t=0.135}} \right. \ => \ \left \{ {{a=-(38.2)/(t) } \atop {19.1t-38.2t=0.135}} \right. \ => \ \left \{ {{a=-5404.6} \atop {t=0.007}} \right.`

finally, a≈-5404.6 [m/s²].

2. Determine the force applied by Alejandro.

the energy is:

`E=(mv^2)/(2); \ or E=FS, where \ m-the \ mass; \ v-velocity; \ F-required \ force; S-distance;`

According to these two equations, the required force is:

`F=(E)/(S)=(mv^2)/(2S);`

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.