Two carts with masses of 4.2 kg and 3.2 kg move toward each other on a frictionless track with speeds of 5.4 m/s and 4.5 m/s, respectively. the carts stick together after colliding head-on. find their final speed. answer in units of m/s.

the final speed is 5.01 m/s

Explanation:

Momentum is the product of mass and velocity.

Cart 1 has a mass of 4.2kg and a speed 5.4 m/s

Cart 2 has a mass of 3.2kg and a speed 4.5 m/s

Total momentum before collision is

m1u1 + m2u2. It becomes

4.2×5.4 + 3.2×4.5 = 22.68 + 14.4

= 37.08kgm/s

The carts stick together after colliding head-on. This means that they move with a common velocity, v. Therefore, Total momentum after collision is (m1 + m2)v. It becomes

(4.2 + 3.2)v = 7.4v

According the the law of conservation of momentum, the total momentum before collision = the total momentum after collision. Therefore,

7.4v = 37.08

v = 37.08/7.4 = 5.01 m/s