Two carts with masses of 11.7 kg and 2.5 kg move in opposite directions on a frictionless horizontal track with speeds of 6.6 m/s and 3.1 m/s, respectively. the carts stick together after colliding head-on. find their final speed. answer in units of m/s.

5.98m/s

Explanation:

Since the two bodies collides, we go by the law of conservation of momentum which states that the sum of momentum of the body before collision is equal to their momentum after collision. Note that the two bodies moves with the same velocity (v) after colliding.

Let m1 and m2 be the masses of the two carts and u1 and u2 be their velocities respectively. If v is their common velocities, according to the law above

m1u1+m2u2 = m1v+m2v

Note that momentum = mass × velocity

Given m1 = 11.7kg m2 = 2.5kg u1 = 6.6m/s u2 = 3.1m/s final speed (v) = unknown

Substituting this values in the formula we have

11.7(6.6)+2.5(3.1) = (11.7+2.5)v

77.22+7.75 = 14.2v

84.97 = 14.2v

V = 84.97/14.2

V = 5.98m/s

Their final speed is 5.98m/s