Question

A football punter accelerates a football from rest to a speed of 13 m/s during the time in which his toe is in contact with the ball (about 0.24 s). If the football has a mass of 0.49 kg, what average force does the punter exert on the ball?_____ N

Answer 1

Given:

The initial speed of the football is: vi = 0 m/s (as initially, the football is at rest)

The final speed of the football is: vf = 13 m/s

The time for which the football accelerates is: t = 0.24 s

The mass of the football is: m = 0.49 kg

To find:

The force exerted on the ball

Step-by-step explanation:

The acceleration of the ball can be determined by using the following equation.

`a=(v_f-v_i)/(t)`

Substituting the values in the above equation, we get:

`\begin{gathered} a=\frac{13\text{ m/s}-0\text{ m/s}}{0.24\text{ s}} \\ \\ a=\frac{13\text{ m/s}}{0.24\text{ s}} \\ \\ a=54.17\text{ m/s}^2 \end{gathered}`

The force exerted by the punter on the ball can be determined by using Newton's second law of motion.

According to Newton's second law of motion,

`F=ma`

Substituting the values in the above equation, we get:

`\begin{gathered} F=0.49\text{ kg}*54.17\text{ m/s}^2 \\ \\ F=26.54\text{ N} \end{gathered}`

Final answer:

The force exerted by the punter on the ball is 26.54 Newtons (N).