Elastic Collision of two objects

[Bowenj]

Homework Statement

A 5.5 kg object moving in the +x direction at 5.5 m/s collides head-on with a 2.5 kg object moving in the -x direction at 4.0 m/s. Find the final velocity of each mass for each of the following situations. (Take the positive direction to be +x.) The equation is elastic

Homework Equations

m1v1+m2v2=m1v1'+m2v2'

.5m1(v1)2+.5m1(v1)2= 5m1(v1')2+5m2(v2)2

The Attempt at a Solution

I plugged the numbers into the first equation, and solved for v2', which gave me 8.1-2.2v1'=v2'

Then i substitued this into the second equation, which gave me
103.1875=.5(5.5)(v1')^2+(.5)(2.5)(8.1-2.2(v1'))^2

then i simplified and go

103.1875 = 2.75(v1')^2+1.25(65.61-35.64v1'+4.84(v1')^2)

I simplified again and got

0= 8.8(v1')^2-44.55v1'-21.175

Okay so then i used the quadratic equation and got 5.51 and -.448, but neither one of those answers are right.

 

[Doc Al]

0= 8.8(v1')^2-44.55v1'-21.175

Okay so then i used the quadratic equation and got 5.51 and -.448, but neither one of those answers are right.

Double check your solution for that quadratic. Your answers are off a bit. (And solving that quadratic correctly does give the correct answer, so your work up to that point is good.)