Quiz4U! Find the velocity after impact?

Question

Suppose that a defensive football player of mass 70 kg collides with a wide receiver of mass of mass 80 kg in mid air. Assume that the velocity of the defensive player is

[5 7 2] and that of the receiver is [-3 -5 4]. If the defensive player grabs onto the receiver upon impact, so that this is a perectly inelastic collision, find their velocity right after impact.

Hint: Use conservation of momentum and that their final velocities are equal (since they are stuck together upon impact, perfectly inelastic collisison).

Possible Answers:

[2.6 2.55 -3.15]

[1.44 2.6 4.5]

[0.73 0.6 3.07]

[-1.44 -2.6 -4.5]

[8.1 -5.3 7.78]

Answer 1

(5*70-3*80)/(70+80) = .7333, so the 3rd choice is the only one possible.

Answer 2

conservation of momentum=m1v1+m2v2=Mv12

Where M=m1+m2 and v12 is the velocity after the collision.  We know everything but v12 which we are solving for through simple algebra.

70*[5 7 2] + 80*[-3 -5 4] = 150(v12)

(70/150)*[5 7 2] + (80/150)*[-3 -5 4] = (v12)

[7/3 49/15 14/15]+[-8/5 -8/3 32/15] =(v12)

now add those together...

[11/15 3/5 46/15]=v12

[0.73 0.6 3.07]=v12