wo ice skaters, Daniel (mass 70.3 kg) and Rebecca (mass 49.6 kg) are practicing.

Question

wo ice skaters, Daniel (mass 70.3 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 12.7 m/s before she collides with him. After the collision, Rebecca has a velocity of magnitude 6.7 m/s at an angle of 53.9° 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?
  m/s
  ° (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?
J

Explanation / Answer

Let v = Daniel's velocity after the collision at an angle theta 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.

=> (49.6) * (12.7) = (49.6) * (6.7) * cos(53.9) + (70.3) * vcos(theta)

=> (70.3) * vcos(theta) = 434.12

=> v cos = 6.175 ... (1)

and (49.6) * (6.7) * sin(53.9) = (70.3) * vsin

=> v sin = 3.819 ... (2)

Squaring and adding equations (1) and (2),

v^2 = 52.715 => v = 7.26 m/s.

and tan = (3.819)/(6.175) = 0.6184

=> theta = 31.73 degrees

Change in KE = (1/2)*[ (49.6) * (12.7)^2 - (49.6)*(6.7)^2 - (70.3)*(7.26)^2 ] J

= 1034.04 J

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