Two ice skaters, Daniel (mass 70.3 kg) and Rebecca (mass 50.1 kg) are practicing

Question

Two ice skaters, Daniel (mass 70.3 kg) and Rebecca (mass 50.1 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 6.9 m/s at an angle of 55.5° 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?
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

a) Using Momentum Conservatiopn theorem - Initial Momentum in X Direction - Initial speed of Daniel = 0 Initial speed of Rebecca = 12.7m/s Initial Momentum in X Direction = 70.3 * 0 + 50.1 * 12.7 = 636.27 Final momentum in X Direction - Let Final speed of Daniel = V cos(alpha) Final speed of Rebecca = 6.9 cos(55.5) = 3.91 m/s Final Momentum in X Direction = 70.3 * V cos(alpha) + 50.1 * 3.91 = 70.3V cos(alpha) + 195.8 Initial Momentum = Final Momentum 636.27 = 70.3V cos(alpha) + 195.8 V cos(alpha) =6.27 m/s -----------1 Initial Momentum in y Direction = 0 (No Movement) Final Momentum in y Direction = 70.3 * V sin(alpha) - 50.1 * 6.9 * sin(55.5) 0 = 70.3 * V sin(alpha) - 284.89 V sin(alpha) = 4.05 m/s -----------2 Dividing 2/1 - tan(alpha) = 4.05/6.27 alpha = 32.86 Degree V sin(32.86) = 4.05 V = 7.464 m/s Daniel's velocity after the collision = 7.464 m/s and Direction is 32.86 degree Clockwise from Rebecca's original direction of motion. b) Initial Kinetic Energy = 1/2 * 50.1 * 12.7^2 Initial Kinetic Energy = 4040.31 J Final Kinetic Energy = 1/2 * 50.1 * 6.9^2 + 1/2 * 70.3 * 7.464^2 Final Kinetic Energy = 3150.88j Change in total Kinetic Energy = 4040.31 - 3150.88 = 889.43 J Change in total Kinetic Energy = 889.43 J

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