Two ice skaters, Daniel (mass 70.0kg ) and Rebecca (mass 45.0kg ), are practicin

Question

Two ice skaters, Daniel (mass 70.0kg ) and Rebecca (mass 45.0kg ), are practicing. Daniel stops to tie his shoelace and, while at rest, is struck by Rebecca, who is moving at 12.0m/s before she collides with him. After the collision, Rebecca has a velocity of magnitude 8.00m/s at an angle of 54.1? from her initial direction. Both skaters move on the frictionless, horizontal surface of the rink.

Exercise 8.27 Part B Two ice skaters, Daniel (mass 70.0kg ) and Rebecca (mass 45.0kg ), are practicing. Daniel stops to tie his shoelace and, while at rest, is struck by Rebecca, who is moving at 12.0m/s before she collides with him. After the collision, Rebecca has a velocity of magnitude 8.00 m/s at an angle of 54.1° from her initial direction. Both skaters move on the frictionless, horizontal surface of the rink. What is the direction of Daniel's velocity after the collision? --41.6 from the Rebecca's original direction Submit My Answers Give Up Correct Part C What is the change in total kinetic energy of the two skaters as a result of the collision? Submit My Answers Give Up Incorrect Try Again; 5 attempts remaining

Explanation / Answer

Linear momentum is conserved.
Consider R's initial direction to be the x-axis.
vR1x = 12.0 m/s
vR2x = (7.00 m/s) cos(54.1 deg) = 4.1046 m/s
vR2y = (7.00 m/s) sin(54.1 deg) = 5.6703 m/s
Momentum components are
pR1x = (12.0 m/s)(45 kg) = 540 kg m/s
pR2x = (4.1046 m/s)(45 kg) = 184.707 kg m/s
pR2y = (5.6703 m/s)(45 kg) = 255.163 kg m/s

Thus, the components of Daniel's momentum after the collision are
pD2x = (540 - 184.707) kg m/s = 355.293 kg m/s
pD2y = -255.163 kg/ms
The components of Daniel's velocity after the collision are found by dividing out his 70-kg mass:
vD2x = 5.0756 m/s
vD2y = -3.6452 m/s

Magnitude of vD2 = sqrt(5.0756^2 + 3.6452^2)
= 6.25 m/s
Direction of vD2 = arctan(-3.6452/5.0756)
= -35.7 degrees, i.e., 89.8 degrees from Rebecca's new direction, or 35.7 deg from her old direction (but turned in the opposite sense from the way she turned)

Kinetic energy: the 90-degree separation suggests that almost no kinetic energy was lost, but you should figure out (1/2)mv^2 for each skater after the collision, and subtract their sum from the original KE of (1/2)(45 kg)(12.0)^2 = 3240 J.

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