Question

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.)

Answer 1

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

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

$v$ - ?

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)

$p_1+p_2=p$

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

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)