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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? How would you find your answer?

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Answer:

They traveling at  along the direction of 55 kg kid.

Step-by-step 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.

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

This is a conservation of momentum problem. The equation relevant here is

[tex]\[m_1v_1+m_2v_2=\left ( m_1+m_2 \right )v_f\][/tex]

where m is the mass and v is the velocity. Because Amy and Jenny move as one mass after crashing (or colliding) with each other, this is an inelastic collision. What we to find is the final velocity, [tex]v_f[/tex], of both Amy and Jenny as a single body.

[tex]v_f=\frac{m_1v_1+m_2v_2}{\left ( m_1+m_2 \right )} = \frac{(55)(3)+(40)(5)}{(55+40)} = \text{3.84 m/s}.[/tex]

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