Mass Velocity and direction of First Block

Question

A 2.50-kg cart slides across a frictionless horizontal surface with an initial speed of 3.00 m/s.

After an elastic head-on collision with an initially stationary cart, that second cart of unknown

mass moves forward with a speed equal to 5.00 m/s. What are the mass, m, of the second block

and the velocity—including the direction—of the first block?

Answer 1

Assume all motion is in 1D ... Use conservation of momentum to write 2.5*3+0 = 5*m+v₁*2.5 where v₁ is the velocity of the first cart and m is the mass of the second. Since the collision is described as "elastic" it can be assumed that energy was conserved as well and that can be used to write .5*3*2.5²+0 = .5*m*5²+.5*2.5*v₁² .

Solving the two equations yields m=1.30 kg and v₁=0.41 m/s