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

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 14.0m/s before she collides with him. After the collision, Rebecca has a velocity of magnitude 8.00m/s at an angle of 52.1? 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?

Explanation / Answer

before collision

initial momentum = Pix = mr*vr = 45*14 = 630 kg m/s

piy = 0

after collision

final momentum = Pfx = 45*8*cos52.1 + 60*Vd*costheta

Pfy = 45*8*sin52.1 + 60*Vd*sin theta

from momentum conservation

Piy = Pfy

45*8*sin52.1 + 60*Vd*sin theta = 0

60*Vd*sin theta = -284.1

vd*sintheta = -4.735

Pfx = Pix

45*8*cos52.1 + 60*Vd*costheta = 630

vd*sintheta = 6.81 m/s

par4t(A)

vd = sqrt(4.735^2+6.81^2) = 8.3 m/s

------

part (B)

theta = tan^_1(4.735/8.3) = 29.7 degrees with the initial direction

---------------------

part(C)

KEi = 0.5*45*14^2 = 4410 J

KEf = (0.5*45*8^2)+(0.5*60*8.3^2) = 3506.7 J

change = KEf - KEi = 903.3 J <----------answer

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