Question

A child of mass 25 kg is skating fast, +10 m/s, and tries to get revenge by colliding with the 60 kg adult who is sitting still. After the collision, the adult goes forward at 6 m/s. What is the child's final velocity?

Answer 1

Answer: -4.4 m/s

Step-by-step explanation:

This problem can be solved by the Conservation of Momentum principle, which establishes that the initial momentum
`p_(o)` must be equal to the final momentum
`p_(f)`:

`p_(o)=p_(f)` (1)

Where:

`p_(o)=m_(1)V_(o)+m_(2)U_(o)` (2)

`p_(f)=m_(1)V_(f)+m_(2)U_(f)` (3)

`m_(1)=25 kg` is the mass of the child

`V_(o)=10 m/s` is the initial velocity of the child

`m_(2)=60 kg` is the mass of the adult

`U_(o)=0 m/s` is the initial velocity of the adult (it is sitting still)

`V_(f)` is the final velocity of the child

`U_(f)=6 m/s` is the final velocity of the adult

Substituting (2) and (3) in (1):

`m_(1)V_(o)+m_(2)U_(o)=m_(1)V_(f)+m_(2)U_(f)` (4)

Isolating
`V_(f)`:

`V_(f)=(m_(1)V_(o)-m_(2)U_(f))/(m_(1))` (5)

`V_(f)=((25 kg)(10 m/s)-(60 kg)(6 m/s))/(25 kg)` (6)

Finally:

`V_(f)=-4.4 m/s` This means the velocity of the child is in the opposite direction