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?

Step-by-step explanation:

The initial momentum of Jack and Leon is,

`\begin{gathered} P_i=m_1u_1+m_2u_2 \\ =45*2+90*7.0 \\ =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* v_1+90*1.0 \\ =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=(720-90)/(45) \\ v_1=14\text{ m/s} \end{gathered}`

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