Question

1. a baseball gets hit by a bat. the velocity of the ball changes by 120 m/s. the time the ball was being hit was 0.2 seconds. the mass of the ball is 1 kg. what was the average force the ball felt during the hit?
2. a basketball hits you in the head. the impulse the ball feels is 50 ns. the velocity of the ball changed by 10 m/s. what was the mass of the ball?

Explanation:

Problem 5

Step1: Recall the impulse - force formula

The impulse - force formula is \(J = F\Delta t\), and also \(J=\Delta p=m\Delta v\). So, \(F\Delta t=m\Delta v\).

Step2: Solve for the force \(F\)

We need to find \(F\). Rearranging the formula \(F\Delta t=m\Delta v\) for \(F\), we get \(F=\frac{m\Delta v}{\Delta t}\).
Given \(m = 1\space kg\), \(\Delta v=120\space m/s\), and \(\Delta t = 0.2\space s\).
Substitute the values into the formula: \(F=\frac{1\times120}{0.2}\).

Step3: Calculate the value of \(F\)

\(F=\frac{120}{0.2}=600\space N\)

Step1: Recall the impulse - momentum formula

The impulse - momentum formula is \(J=\Delta p=m\Delta v\).

Step2: Solve for the mass \(m\)

We need to find \(m\). Rearranging the formula \(J = m\Delta v\) for \(m\), we get \(m=\frac{J}{\Delta v}\).
Given \(J = 50\space Ns\) and \(\Delta v=10\space m/s\).
Substitute the values into the formula: \(m=\frac{50}{10}\).

Step3: Calculate the value of \(m\)

\(m = 5\space kg\)

Answer:

\(600\space N\)

Problem 6