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? v =   m/s   SubmitMy AnswersGive Up Part B What is the direction of Daniel's velocity after the collision? θ =   ∘ from the Rebecca's original direction SubmitMy AnswersGive Up Part C What is the change in total kinetic energy of the two skaters as a result of the collision?

Answer 1

a)

Let v = Daniel's velocity after the collision at an angle θ 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 cosθ

=>630=216 + (65) * v cosθ

=>414/65 = v cosθ

=> v cosθ = 6.36 ... (1)

and (45) * (8) * sin(53.1°) = (65) * v sinθ
=> v sinθ = 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

tanθ = (4.42)/(6.36) = 0.69 => θ = 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.