Question

A 95 kg fullback, running at 8.2 m/s, collides in midair with a 128 kg defensive tackle moving in the opposite direction. Both players end up with zero speed.
A) What was the change in the fullbacks momentum?
B) What Was the change in the defensive momentum?
C) What was the defensive tackle's original momentum?
D) How fast was the defensive tackle moving origianally?

Answer 1

let \(m_1=95kg\) represent the mass of the fullback, \(v_{11}=8.2m/s\) represent the fullbacks initial velocity, \(v_{12}=0m/s\) represent the fullbacks final velocity, \(m_2=128kg\) represent the defensive players mass, \(v_{21}\) represent the defensive players initial velocity, \(v_22=0m/s\) represent the defensive players final velocity. then, using conservation of momentum, we get:\[m_1*v_{11}+m_2*v_{12}=m_1*v_{12}+m_2*v_{22}\]\[\therefore 95*8.2+128*v_{12}=0\quad\text{since both }v_{12}\text{ and }v_{22}\text{ are zero}\]\[\therefore v_{12}=-\frac{95*8.2}{128}=-\frac{779}{128}=-6\frac{11}{128}\text{ m/s}\]
A) change in fullbacks momentum = final momentum - initial momentum = 0 - 95*8.2 = -779.
B) change in defensive players momentum = change in fullbacks momentum (since both players end up with zero speed) = -779.
C) defensive players original momentum = - fullbacks initial momentum (since both players end up with zero speed) = -(95*8.2) = -779.
D) \(v_{12}=-6\dfrac{11}{128} m/s\)

Answer 2

Use the convservation of linear momentum principle; so Pin=Pf
so at the end since they have no velocity, there is no kinetic energy at the end so you know that Eki=0 and Pin=0 The change in kinetic is simply Final - Initial :) follow the steps above and your good :)