momentum question?

Question

Two ice skaters, Daniel (mass 69.9 kg) and Rebecca (mass 49.6 kg) are practicing. Daniel stops to tie his shoelace and, while at rest, is struck by Rebecca, who is moving at 13.4 m/s before she collides with him. After the collision, Rebecca has a velocity of magnitude 7.1 m/s at an angle of 52.1° from her initial direction. Both skaters move on the frictionless, horizontal surface of the rink.

(a) What are the magnitude and direction of Daniel's velocity after the collision?

(b) angle° (clockwise from Rebecaa's original direction of motion)

(c) What is the change in total kinetic energy of the two skaters as a result of the collision?

Answer 1

Momentum is conserved, so
49.6*13.4=49.6*7.1*cos(52.1)+69.9*v*cos(th)
where v is Daniel's speed
and th is the angle from Rebecca's direction

also
0=49.6*7.1*sin(52.1)+69.9*v*sin(th)
solve first for tan(th)


v*cos(th)=6.356

v*sin(th)=3.975

Tan(th)=0.62545
th=32.02397 degrees


v=7.5 m/s

KEi=.5*49.6*13.4^2
=4453 J


KEo=.5*(49.6*7.1^2+69.9*7.5*2)
=1774 J

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