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

Question

Two ice skaters, Daniel (mass 60.0 kg ) and Rebecca (mass 45.0 kg ), are practicing. Daniel stops to tie his shoelace and, while at rest, is struck by Rebecca, who is moving at 14.0 m/s before she collides with him. After the collision, Rebecca has a velocity of magnitude 6.00 m/s at an angle of 55.1 from her initial direction. Both skaters move on the frictionless, horizontal surface of the rink.

1.What is the magnitude of Daniel's velocity after the collision?

2. What is the direction of Daniel's velocity after the collision?

3. What is the change in total kinetic energy of the two skaters as a result of the collision?

Explanation / Answer

Before collision,

velocity of rebecca, u = 14 m/s i

velocity of Daniel = 0

now using momentum conservation for collision,

60 x 0 + 45 x 14i = 45 x 6(cos55.1i + sin55.1j) + 60vD

vD = 7.93i - 3.69j m/s

1. Magnitude of velocity = sqrt(7.93^2 + 3.69^2) = 8.75 m/s

2 .direction = tan^-1(3.69 / 7.93) = 24.95 deg from initial direction of rebecca

3. initial KE = 0 + 45x14^2 /2 = 4410 J

final KE = (60 x 8.75^2 /2 ) + (45 x 6^2 /2 ) = 3106.87 J

change in KE = - 1303.12 J

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