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

Answer:

$v_2=-8.33m/s$

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:

$v_2=-\frac{m_1v_1}{m_2}=-\frac{(150Kg)(5m/s)}{(90Kg)}=-8.33m/s$

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