Answer to Question #109515 in Mechanics | Relativity for dagdf

Question #109515
Hobbes, the stuffed tiger, has a mass of 28.4 kg. Calvin, the little boy, has a mass of 17.7 kg. In a game of football, Hobbes runs to the right (towards Calvin) at 9.2 m/s. Calvin runs to the left (towards Hobbes) at 12.0 m/s. The two collide and stick together.

What is their final velocity? (Assume that velocities to the right are positive.)
Expert's answer

"m_1=28.4 \\ kg, \\ v_1=9.2\\ m\/s"

"m_2=17.7 \\ kg, \\ v_2=-12.0\\ m\/s"

"v" - ?

We will use the fact that:

When two objects collide the total momentum before the collision is equal to the total momentum after the collision.

"p_1=m_1v_1" - momentum of Hobbes

"p_2=m_2v_2" - momentum of Calvin

"p_1+p_2" - total momentum (before collision)

"p=mv=(m_1+ m_2)v" - final momentum (after collision)



We have "\\ \\ v=\\frac{m_1v_1+m_2v_2}{m_1+m_2}"

"v=\\frac{28.4\\times 9.2-17.7\\times 12.0}{28.4+17.7}=1.06 \\ m\/s"

Answer: 1.06 m/s (to the right)

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