A 2589-kg van runs into the back of a 825-kg compact car at rest. They move off together at 8.5 m/s. Assuming the friction with the road is negligible, calculat

Question

how would you solve a problem like this?

Answer 1

I assume you want to find the initial velocity of the 2589 kg van.  Use conservation of linear momentum, which still applies here even though the collision is not elastic.  

 

Initial state:  m1 = 2589 kg, moving toward m2 at unknown speed v1

m2 = 825 kg at rest

 

Final state:  Total mass m1+m2 moving at vf = 8.5 m/s

 

Momentum conservation:  pi = pf

 

m1 * v1 = (m1 + m2) * vf

 

Hence,

 

v1 = [(m1 + m2) * vf / m1] = [(2589 + 825) * 8.5 / 2589] m/s = 11.21 m/s