Momentum and Velocity

Question

Two masses traveling from opposite directions collide, forming a single stationary mass. Of the first mass is three times greater than the second mass, how much faster was the second mass traveling at the time of collision?

Answer 1

Momentum is conserved meaning that the momentum before the collision equals the momentum after the collision. The momentum after the collision is zero because the combined mass is "stationary".

So the momentum before the collision must add to zero.

Momentum equals mass times velocity (P = mv) So let "m" represent the mass of object #2 then the mass of object 1 is "3m". Let v be the velocity of object 1 then and let k•v be the velocity of object 2 where "k" is the multiplier of object 1's velocity (the "how much faster" multiplier being asked for)

The momentum before the collision then is P = (3m)(v) + (m)(k•v) and that must be zero

(3m)(v) + (m)(k•v) = 0

kmv = -3mv

Divide both sides by "mv" to get:

k = -3

So object 2 is traveling 3 times faster than object 1 but in the opposite direction.