Question

# Two ice skaters, Daniel (mass = 65.0 kg) and Rebecca (mass = 45.0 kg) are practicing...

Two ice skaters, Daniel (mass = 65.0 kg) and Rebecca (mass = 45.0 kg) are practicing on the ice. Daniel stops to tie his lace, and while at rest he is struck by Rebecca, who is moving 12.0 m/s before she collides with him. After the collision, Rebecca is moving forward at 8.50 m/s at a 53 degree angle with respect to her initial direction. What is the velocity vector (magnitude and direction, or x- and y-components) of Daniel after the collision? Assume frictionless ice. Hint: Momentum is conserved separately in both the x- and y-directions.

Let, Mr= Rebecca's mass = 45 kg

Md = Danial's mass = 65 kg

Vri = Rebecca's initial velocity =12 m/s

Vrf = Rebecca's final velocity = 8.50 m/s

r = 53°

Initial momentum situation is:

1) Lxi = Mr×Vri.

2) Lyi =0

Final momentum equation is:

3) Lxf = Mr×VrfCosr +Md×Vdxf

4) Lyf = MrVrfSinr + MdVdyf

Conservation of momentum in each of the two dimensions implies following:

Lxi =Lxf

i.e 5)MrVri = MrVrfCosr +Mdxf

Lyi = Lyf

i.e 6)0= MrVrfSinr + MdVdyf

solving (5) for Vdxf:

Vdxf = (MrVri- MrVrfCosr)÷ Md

= (45×12- 45×8.50×cos53)÷65

= 4.77 m/s

Solving (6) for Vdyf :

Vdyf = - (45×8.50×Sin53)÷65

= -4.69 m/s

Danial's final angle of motion :

d = tan-1(-4.699/4.77) = 44.57°

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