Question

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.

Answer 1

Let, M_r= Rebecca's mass = 45 kg

M_d = Danial's mass = 65 kg

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

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

_r = 53°

Initial momentum situation is:

1) L_xi = M_r×V_ri.

2) Ly_i =0

Final momentum equation is:

3) L_xf = M_r×V_rfCos_r +M_d×V_dxf

4) L_yf = M_rV_rfSin_r + M_dV_dyf

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

L_xi =L_xf

i.e 5)M_rV_ri = M_rV_rfCos_r +M_dxf

L_yi = L_yf

i.e 6)0= M_rV_rfSin_r + M_dV_dyf

solving (5) for V_dxf:

V_dxf = (M_rV_ri- M_rV_rfCos_r)÷ M_d

= (45×12- 45×8.50×cos53)÷65

= 4.77 m/s

Solving (6) for V_dyf :

V_dyf = - (45×8.50×Sin53)÷65

= -4.69 m/s

Danial's final angle of motion :

_d = tan^-1(-4.699/4.77) = 44.57°