Question

A big defensive lineman picks up a fumbled football and begins rumbling toward the end zone. His mass is 150 kg, and his velocity is 5.0 m/s, west. A brave wide receiver, whose mass is 90 kg, must stop that lineman and he is right in the lineman's path, so it has to be a head-on collision. How fast must the wide receiver be running if he wants to drop the lineman in his tracks and save the day?

Answer 1

`v_2=-8.33m/s`

Step-by-step explanation:

The linear momentum during this collision must be conserved, which means that momentum before and after the collision must be the same.

We have a big defensive lineman of mass
`m_1=150Kg` and velocity
`v_1=5m/s` going in what we will call the positive direction, and a wide receiver of mass
`m_2=90Kg` and velocity
`v_2` which we don't know. Since the collision is head on, momentum before the collision will be
`p_i=m_1v_1+m_2v_2`

After the collision, the receiver drops the lineman in his tracks, which means they come to a stop, so the momentum is null, and since this momentum must be equal to the one before the collision we have:

`p_i=0=m_1v_1+m_2v_2`

Which means:

`m_1v_1=-m_2v_2`

So for
`v_2` we have:

`v_2=-(m_1v_1)/(m_2)=-((150Kg)(5m/s))/((90Kg))=-8.33m/s`

where the negative sign indicates its opposite to our positive direction (of the big defensive lineman).