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 14.0m/s before she collides with him. After the collision, Rebecca has a velocity of magnitude 6.00m/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

apply the law of conservation of angular momentum as

m1u1 cos theta + m2u2 cos = MV

45*14 =   45 * 6 cos(52.1)+ 70 *v*cos theta

so Vcos theta = 464.14/70

Vcostheta = 6.63

also for Rebecca diurection

0=45 * 6 *sin(52.1)+70 *v*sin theta

v sin theta = -3.04

so tan theta = 3.04/6.63 = 0.459

theta = 24.65 deg   direction of Daniel

so v = 6.64/cos 24.65

v = 7.3 m/s    velocity of Daneil

initiak KE = 0.5 mv^2 = 0.5 * 45 * 14*14 = 4410 Joules

final KE = 0.5(m1u1^2 + m2u2^2)

KEf = 0.5*(( 45 * 6 *6 ) + ( 70 * 7.3*7.3))

KEf = 2675.15 Joules

Change in KE = 2675.15-4410 1734.85 Joules

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