A 2.40 kg can of coffee moving at 1.50 m/s in the + x-direction on a kitchen counter collides head-on with a 1.20 kg box of macaroni that is initially at rest. After the collision the can of coffee is moving at 0.825 m/s in the + x-direction. What is the velocity (magnitude and direction) of the box of macaroni after the collision?

The macaroni travels with a velocity of 1.35 m/s in the + x-direction.

Explanation:

By the conservation of momentum principle and assuming there is no external force (e. g. friction) acting on the system, the total initial momentum is equal to the total final momentum.

We take all velocities in the + x-direction as positive.

Initial momentum of coffee can = (2.40 kg) (1.50 m/s) = 3.60 kg m/s

Initial momentum of macaroni = (1.20 kg) (0.00 m/s) = 0.00 kg m/s

Total initial momentum = (3.60 + 0.00) kg m/s = 3.60 kg m/s

Final momentum of coffee can = (2.40 kg) (0.825 m/s) = 1.98 kg m/s

Final momentum of macaroni = (1.20 kg) (v m/s) = 1.20v kg m/s

Total final momentum = (1.98 + 1.20v) kg m/s

Equating both initial and final total momenta,

3.60 kg m/s = (1.98 + 1.20v) kg m/s

1.20v kg m/s = 1.62 kg m/s

v = (1.62 kg m/s) : (1.20 kg) = 1.35 m/s

Since this is positive, the macaroni travels with a velocity of 1.35 m/s in the + x-direction.