Question

Running at 2 m/sec, Jack, the 45-kg quarterback, collides with Leon, the 90-kg tackle, who is traveling towards him at 7.0 m/sec. Upon colliding, Leon continues to travel forward towards Jack, at 1.0 m/sec. How fast is Jack knocked backwards?

Answer 1

Given:

The mass of Jack is,

$m_1=45\text{ kg}$

The initial speed Jack is,

$u_1=2\text{ m/s}$

The mass of Leon is

$m_2=90\text{ kg}$

The initial speed of Leon is

$u_2=7.0\text{ m/s}$

The final speed of Leon after the collision is

$v_2=1.0\text{ m/s}$

To find:

How fast is Jack knocked backward?

Explanation:

The initial momentum of Jack and Leon is,

$\begin{gathered} P_i=m_1u_1+m_2u_2 \\ =45\times2+90\times7.0 \\ =720\text{ kg.m/s} \end{gathered}$

If the speed Jack after the collision is

$v_1$

the final momentum is

$\begin{gathered} P_f=m_1v_1+m_1v_2 \\ =45\times v_1+90\times1.0 \\ =45v_1+90\text{ kg.m/s} \end{gathered}$

Applying, The total linear momentum before the collision is the sum of the momentums of each of the football players. So,

$\begin{gathered} 45v_1+90=720 \\ v_1=\frac{720-90}{45} \\ v_1=14\text{ m/s} \end{gathered}$

Hence, Jack is knocked backward at 14 m/s.