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

$100\: mph=100\cdot44.704=4470.4\: \frac{cm}{s}$

The initial momentum is given by

$\begin{gathered} p_1=m_1\cdot u_1+m_2\cdot u_1 \\ p_1=0.145\cdot4470.4+65\cdot0 \\ p_1=648.21\: \frac{\operatorname{kg}\cdot cm}{s} \end{gathered}$

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,

$\begin{gathered} p_2=65.145\cdot v_2 \\ 648.21=65.145\cdot v_2 \\ v_2=\frac{648.21}{65.145} \\ v_2=9.9\: \frac{cm}{s} \end{gathered}$

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