Question

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?

Answer 1

The action of crashing would lower the speed by at least half so 1.5 + 2.5 = 4. But since you do not know in which way they crashed I would just say that this question is not telling how much they slow down so, I would just do 5 m/s + 3 m/s = 8 m/s travelling in the direction Amy was moving but since the larger mass would move the smaller mass and adjust I'd say they are both moving at 3 m/s.

Answer 2

They traveling at
`-0.37\ m.s^(-1)` along the direction of 55 kg kid.

Explanation:

Conservation of momentum-

Momentum of a system is constant if there are no external forces acting on the system.

As they crash into each other and hold onto each other so that they move as one mass and no other force is acting on them, so conservation of momentum can be applied here.

`\Rightarrow m_1u_1+m_2u_2=(m_1+m_2)v`

`\Rightarrow 55\cdot 3+40\cdot (-5)=(55+40)\cdot v`

`\Rightarrow 165-200=95\cdot v`

`\Rightarrow 95\cdot v=-35`

`\Rightarrow v=-0.37\ m.s^(-1)`

The final direction of velocity will be opposite to the assumed direction of the mass of 40 kg.