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 12.0m/s before she collides with him. After the collision, Rebecca has a velocity of magnitude 8.00m/s at an angle of 55.1? 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?   ? from the Rebecca's original direction

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

Explanation / Answer

Initial velocity of Daniel uD = 0

Initial Velocity of Rebecca uR = 12 i m/s

Final velocity of Danial vD = vD(cos@ i + sin@j)

Final velocity of Rebecca vR = 8 ( cos55.1 i + sin55.1 j) = 4.58 i + 6.56j m/s

Uisng momentum conservation,

mD * uD + mR * uR = mD*vD   + mR *vR

60 * 0 + 45 * 12i   = 60 ( vDcos@i + vDsin@ j) + 45( 4.58 i + 6.56j )

vDcos@ i + vDsin@ j = 5.57 i - 4.92 j

so vD sin@ = - 4.92

vD cos@ = 5.57

tan@ = -4.92 / 5.57 = - 41.45 degrees ............Ans ( B)

vD sin41.45 = 4.92

vD = 7.43 m/s   ............Ans (A)

Part C :

change in K.E. = final K.E - initial K.E.

= [ 60 x 7.43^2 /2 + 45 x 8^2 /2 ] - [60 x 0^2 /2 + 45 x 12^2 /2 ]  

= - 143.85 J

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