A 6 kg bug traveling east at 45 m/s is hit head-on by a westbound 67 kg bicyclist on an 11 kg bike going 32 m/s. The biker swallows the bug. What is the resulting velocity of the bug-bike-biker system?

The initial momentum and initial momentum of colliding system is the same. Hence, the final velocity of the bug-bike-biker system will be 32.92 m/s.

What is conservation of momentum ?

The momentum of an object is the product of its mass and velocity. The total momentum of the a system is constant during a collision. Hence total initial momentum is equal to the total final momentum.

Initial momentum of bug = mass × Velocity

p1 = 6 kg × 45 m/s = 270 kg m/s

initial momentum of bike+ biker = 11 kg + 67 kg) × 45 m/s = 2496 kgm/s.

Then total initial momentum = 270 + 2496 kg m/s. = 2766 kg m/s.

Then total final momentum = (m1 + m2)v = 2496 kgm/s.

p2 = (78 kg + 6 kg)v = 2496 kgm/s.

v = 32.92 m/s.

Therefore, the momentum of the bug-bike-biker system after collision is 32.92 m/s.

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