Elastic Cart Collision of a stationary and a moving cart

[Potato21]

I'm having some trouble with some homework and I'm hoping someone can help me.

PROBLEM:
#6. Cart1, with mass m, is initially at rest and is struck by cart2,
which has a mass of 336 kg and initial speed of 1.81 m/s. The collision
is elastic and after the collision cart2 continues to move in its
original direction at 0.807 m/s. Find m, the mass of cart1.
#7.Find the speed of cart1 after the collision.

ATTEMPT AT SOLUTION:

I have calculated that

m1v1+m2v2=m1v1'+m2v2'
m1(0)+336kg(1.81m/s)=m1v1'+336kg(0.807m/s)
m1v1'=336kg(1.81-0.807)
m1v1'=337 kg*m/s

I'm stuck here. I tried calculating the amount of energy the second
cart should have

1/2m2(v2-v2')^2=
0.5(336)(1.81-0.807)^2=169J

and then that

169J=0.5m1(v1)^2 so that

m1=169*2/v1^2

and subbing that into

m1v1'=337 kg*m/s

(169*2/v1'^2)*v1'=337 kg*m/s

338/v1'=337

thus v1' =338/337

This however does not answer #7 and when working backwards to find the
mass it also provides the wrong answer.

Thank you for any assistance you can provide.
Potato21EDIT: Oops, dumb mistake, I got it!

 

[Nate810]

To find the mass of Cart 1, we can rearrange our equation as follows:m1v1'= 336kg(1.81-0.807)m1 = (336kg(1.81-0.807))/(v1')Since v1' = 0.807m/s,m1 = (336kg(1.81-0.807))/(0.807m/s)m1 = 420.9kgTo find the speed of Cart 1 after the collision, we can use conservation of momentum:m1v1 + m2v2 = m1v1' + m2v2'm1*0 + 336kg*1.81m/s = m1*v1' + 336kg*0.807m/sm1*v1' = 336kg*(1.81-0.807)m/sv1' = (336kg*(1.81-0.807m/s))/m1v1' = (336kg*(1.81-0.807m/s))/420.9kgv1' = 0.922m/s