Two ice skaters, Daniel (mass 65.0 kg ) and Rebecca (mass 45.0 kg ), are practic

Question

Two ice skaters, Daniel (mass 65.0 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 8.00 m/s at an angle of 53.1 from her initial direction. Both skaters move on the frictionless, horizontal surface of the rink.

Part A

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

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Part B

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

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Part C

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

Two ice skaters, Daniel (mass 65.0 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 8.00 m/s at an angle of 53.1 from her initial direction. Both skaters move on the frictionless, horizontal surface of the rink.

Part A

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

v =   m/s  

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Part B

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

=    from the Rebecca's original direction

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Part C

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

Explanation / Answer

a)

Let v = Daniel's velocity after the collision at an angle with Rebecca's original direction.

As no external force acted during the collision, initial and final linear momenta of Daniel and Rebecca in the original direction of Rebecca's motion and in a direction perpendicular to it will be the same.

=> (45) * (14) = (45) * (8) * cos(53.1°) + (65) * v cos

=>630=216 + (65) * v cos

=>414/65 = v cos

=> v cos = 6.36 ... (1)

and (45) * (8) * sin(53.1°) = (65) * v sin
=> v sin = 4.42 ... (2)
Squaring and adding equations (1) and (2),
v^2 = 59.98 => v = 7.74 m/s.

magnitude of Daniel's velocity after the collision=7.74 m/s

b) direction of Daniel's velocity after the collision

tan = (4.42)/(6.36) = 0.69 => = 34.60°  from the Rebecca's original direction

c )change in total kinetic energy of the two skaters as a result of the collision
= (1/2) [ (45) * (14)^2 - (45)*(8)^2 - (65)(7.74)^2 ] J
= (1/2)[8820 - 2880 - 3893] j

=1023 J.

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