Question

A 70 kg football player running at 3m/s north tackles an 80kg player running at 1.5 m/s south. what is the magnitude and direction of the entangled players after the collision?
a) .6 m/s north
b) 2.2 m/s north
c) .6 m/s south
d) 2.2 m/s south

Answer 1

It could never actually happen like this, but the question is
looking for you to 'conserve' the momentum.

Momentum of a moving object is (mass) x (velocity).
Like velocity, momentum has a direction.
Momentum is one of those things that's 'conserved'. 
That means that momentum can't appear out of nowhere, and
it doesn't disappear.  The total after the collision is the same as
the total was before the collision.  

Momentum of the skinny player:

                     (70 kg) x (3 m/s north) = 210 kg-m/s north.

Momentum of the heavy player:

                     (80 kg) x (1.5 m/s south)  =  120 kg-m/s south .

Total momentum before the collision is

                     (210 kg-m/s north) + (120 kg-m/s south)

                 =        90 kg-m/s north  .

It has to be the same after the collision.

                       (mass) x (velocity)  =  90 kg-m/s north.

The  mass after the collision is 150 kg, because they get
tangled up and stuck together, and they move together.

                                (150 kg) x (velocity)  =  90 kg-m/s north .

Divide each side
by  150 kg :                   velocity  =  (90 kg-m/s north) / (150 kg)

                                                =  (90/150)  (kg-m/s / kg  north)

                                                 =        0.6 m/s  north  .