Question

Two hockey players skating on essentially frictionless ice collide head-on. Madeleine, of mass 65.0 kg, is moving at 6.00 m/s to the east just before the collision and at 3.00 m/s to the west just after the collision. Buffy, of mass 55.0 kg, is moving at 3.50 m/s to the east just after the collision. Find Buffy's velocity (magnitude and direction) just before the collision.

Answer 1

Explanation:

It is given that,

Mass of Madeleine, $m_1=65\ kg$

Initial speed of Madeleine, $u_1=6\ m/s$ (due east)

Final speed of Madeleine, $v_1=-3\ m/s$ (due west)

Mass of Buffy, $m_2=55\ kg$

Final speed of Buffy, $v_2=3.5\ m/s$ (due east)

Let $u_1$ is the Buffy's velocity just before the collision. Using the conservation of linear momentum as :

$m_1u_1+m_2u_2=m_1v_1+m_2v_2$

$65\times 6+55\times u_2=65\times (-3)+55\times 3.5$

$u_2=-7.13\ m/s$

So, the initial speed of the Buffy just before the collision is 7.13 m/s and it is moving due west. Hence, this is the required solution.