Two ice skaters, Daniel (mass 60.0kg) and Rebecca (mass 45.0kg), are practicing.

Question

Two ice skaters, Daniel (mass 60.0kg) 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 7.00m/s at an angle of 52.1degree from her initial direction. Both skaters move on the frictionless, horizontal surface of the rink.

(A)What is the magnitude of Daniel's velocity after the collision?

(B)What is the direction of Daniel's velocity after the collision?

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

SHOW WORK PLEASE!

Explanation / Answer

Let after collision rebecca's velocity is along y-direction
So rebecca's initial velocity is 52.1o tilted to the y-axis

Conserving momentum in the y-direction;

45*12*cos 52.1 = vy*60 + 45*7 Daniel,s velocity = vx i + vyj

gives vy = 0.2786m/sec

Conserving momentum in the x-direction;

45*12*sin 52.1 = vx*60

vx = 7.102m/sec

So magnitude of velocity = 7.107m/sec

direction of daniel's velocity = tan-1(0.2786/7.102) with the x-axis = 2.246o with the x-axis or 35.654o with the initial direction of Rebecca

Change in total kinetic energy = 1/2 * 45 * 144 - (1/2 * 60 * 50.5 + 1/2 * 45 * 49) = 622.5 J

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