Two ice skaters, Daniel (mass 69.0 kg) and Rebecca (mass 51.0 kg) are practicing. Daniel stops to tie his shoelace and, while at rest, is struck by Rebecca, who is moving at 13.5 m/s before she collides with him. After the collision, Rebecca has a velocity of magnitude 6.3 m/s at an angle of 51.5° 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?
° (clockwise from Rebecca's original direction of motion)
(b) What is the change in total kinetic energy of the two skaters as a result of the collision?
Let v = Daniel's velocity after the collision at an angle θ with Rebecca's original direction.
As no external force acted during the collision, initial and final linear momenta of Daniel and Rebecca in the original
direction of Rebecca's motion and in a direction perpendicular
to it will be the same.
(51)*(13.5) = (51)*(6.3)*cos(51.5°) + (69)*vcosθ
v cosθ = 7.07 ........... (1)
and (51)*(6.3)*sin(51.5°) = (69)*v sinθ
v sinθ = 3.644 .......... (2)
Squaring and adding equations (1) and (2),
v^2 = 63.26
v = 7.95 m/s.
and tanθ = (3.644)/(7.07) = 0.8872
θ = 27.27°
Change in KE = (1/2) [ (51)*(13.5)^2 - (51)*(6.3)^2 - (69)(7.95)^2 ] J
= (1/2) [ 9294.75 - 2024.19 - 4360.97 ]
= 1454.795 J.
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