Question

"Cart 1 has a mass of 2.8 kg and is moving with a velocity of 6.6 m/s[right] along a frictionless track. Cart 2 has a mass of 3.2 kg and is moving at 2.5 m/s[left]. The carts collide in a head-on elastic collision cushioned by a spring with a spring constant of 3.0x10^4 N/m. Calculate the maximum compression of the spring."
Options are: 0.069, 0.041, 0.077, 0.096, 0.064

Ok so I'm having trouble with this question. I keep getting an answer that doesn't fit any options that are given...
I know I have to find the velocity of both carts at max. compression and got 4.413 as my answer:((m1*v1)+(m2*v2))/(m1+m2)
Then I tried calculating for max. compression using this equation:
((m1)(v1)^2 + (m2)(v2)^2 - (m1+m2)(4.413)^2)/k --- (all under the root)
and I got 0.0289 as an answer. What am I doing wrong?

Answer 1

Using conservation of energy (sume of intial KE goes into PE of spring), I get 0.930965108 m, which is not one of the answer either. PS. I disagree with both of the ways you worked it.

Answer 2

The way I solved it was the way the textbook recommended to solve it; this question just had different numbers than the textbook's. That's why I'm confused about how I didn't get the answer. Thanks anyway for your help.