Two ice skaters, Daniel (mass 69.1 kg) and Rebecca (mass 50.7 kg) are practicing

Question

Two ice skaters, Daniel (mass 69.1 kg) and Rebecca (mass 50.7 kg) are practicing. Daniel stops to tie his shoelace and, while at rest, is struck by Rebecca, who is moving at 12.9m/s before she collides with him. After the collision, Rebecca has a velocity of magnitude 6.9 m/s at an angle of 50.7° 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

I solved this problem 2 days ago, when I mentioned smth is wrong with the numbers. The total energy is not conserved, even though should be.

During my work the system blocked, and I could not send the answer. Now I see this question is "with me" ("glued" on me) again. It was the same yesterday, but I thought is smth wrong with the software.

Anyway, I'll give you the equations that allow to find the missing parameters:

Consider 0x the axis for Rebecca's initial movement, and keep this axis as reference for the movemenet after collision:

0x: m1v1=m1v'1cos(50.7)+m2v'2cos(alpha)

0y: m1v'1sin(50.7)=m2v'2sin(alpha)

Using sin2+cos2=1, solve the system and find alpha and v'2.

From the text:

m1=50.7 kg

m2=69.1 kg

v1=12.9 m/s

v'1=6.9 m/s

I got: v'2=7.38 m/s

alpha~32.06 deg

With these values the conservation law of kinetic energy is not respected:

m1v12/2=m1v'12/2+m2v'22/2

Left term is ~ 4218.5

Right term ~ 3088.66

I might mistake the numerical calculus, but rather the numbers from the text are wrongly arranged.

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