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

They traveling at
`0.37\ m/s` in backward direction.

Explanation:

Given mass of Ammy
`m_1=55kg`

and velocity is forward at
`v_1=3m/s`

Also, mass of Jenny
`m_2=40kg`

Who is travelling in opposite direction
`v_2=-5m/s`

Let velocity in forward direction is positive and velocity in backward direction is negative.

Also, velocity after crash is
`v`

As they crashed into each other and they moved as one mass. We can apply principle of conservation of momentum.

Conservation of momentum says momentum before collision should equal to momentum after collision.

`m_1v_1+m_2v_2=(m_1+m_2)v`

`(55*3)+(40*(-5))=(55+40)v\\\\165-200=95v\\\\-35=95v\\\\v=(-35)/(95)=-0.368m/s`

So, velocity after collision
`v`≅
`-0.37m/s` is in opposite direction. That is the direction of Jenny.