A 2.3 kg cart is rolling across a frictionless, horizontal track towards a 1.5 kg cart that is initially held at rest. The carts are loaded with strong magnets that cause them to attract one another. Thus, the speed of each cart increases. At a certain instant before the carts collide, the first cart's velocity is + 4.9 m/s and the second cart's velocity is - 1.9 m/s. a) What is the total momentum of the system of the two carts at this instant? b) What was the velocity of the first cart when the second cart was still at rest?

total momentum = 8.42 kgm/s

velocity of the first cart is 3.660 m/s

Explanation:

Given data

mass m1 = 2.3 kg

mass m2 = 1.5 kg

final velocity V2 = 4.9 m/s

final velocity V3 = - 1.9 m/s

to find out

total momentum and velocity of the first cart

solution

we know mass and final velocty

and initial velocity of second cart V1 = 0

so now we can calculate total momentum that is m1 v2 + m2 v2

total momentum = 2.3 * 4.9 + 1.5 * (-1.9)

total momentum = 8.42 kgm/s

and

conservation of momentum is

m1 V + m2 v1 = m1 v2 + m2 v3

put all value and find V

2.3 V + 1.5 (0) = 2.3 (4.9) + 1.5 (-1.9)

V = 8.42 / 2.3

V = 3.660 m/s

so velocity of the first cart is 3.660 m/s