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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?

1 Answer

5 votes

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

User Robinjohnobrien
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