Two kids are roller skating. Amy, with a mass of 55 kg, is traveling forward at 3 m/s. Jenny, who has a mass of 40 kg, is traveling in the opposite direction at 5 m/s. They crash into each other and hold onto each other so that they move as one mass. How fast are they traveling?

Accepted Solution

7/19 m/sec in Jenny's direction

Assume that the direction of motion of Amy is the default direction given the positive sign.
Therefore. Jenny's direction will be given a negative sign.
The law of conservation of momentum states that: "For a closed system, momentum is conserved.
This means that:
M1V1 + M2V2 = M3V3
M1 is Amy's weight = 55 kg
V1 is Amy's velocity = 3 m/sec
M2 is Jenny's weight = 40 kg
V2 is Jenny's velovity = -5 m/sec
M3 is their final mass = 55+40 = 95 kg
V3 is their final velocity that we want to find

Substitutw with the givens in the above equation to get the final velocity as follows:
(55)(3) + (40)(-5) = 95V3
165 - 200 = 95V3
-35 = 95 V3
V3 = -7/19 m/sec
This means that their final velocity is 7/19 m/sec in Jenny's direction

Hope this helps :)