Question

4.A regulation 145 g baseball can be hit at speeds of 100 mph. If a line drive is hit essentiallyhorizontally at this speed and is caught by a 65 kg player who has leapt directly upward into the air,what horizontal speed does he acquire by catching the ball?4.2 cm/s5.6 cm/s11.8 cm/s9.9 cm/s

Answer 1

We are given the following information:

Mass of ball = 145 g = 0.145 kg

Mass of player = 65 kg

Initial velocity of ball = 100 mph

Let us first convert 100 mph into cm/s

1 mph is equal to 44.704 cm/s

`100\: mph=100\cdot44.704=4470.4\: (cm)/(s)`

The initial momentum is given by

The final momentum is given by

`\begin{gathered} p_2=(m_1+m_2)\cdot v_2 \\ p_2=(0.145+65)\cdot v_2 \\ p_2=65.145\cdot v_2 \end{gathered}`

The total momentum of the system must be conserved so,

`\begin{gathered} p_2=65.145\cdot v_2 \\ 648.21=65.145\cdot v_2 \\ v_2=(648.21)/(65.145) \\ v_2=9.9\: (cm)/(s) \end{gathered}`

Therefore, the player acquires a speed of 9.9 cm/s after catching the ball.