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

m1(Daniel) = 65 kg              m2(Rebeca) = 45 kg

before collision

speeds

u1x = 0                          u2x = 12 m/s

u1y = 0                          u2y = 0

after collision

v1x =                                   v2x = 8.5*cos53

v1y = ?                               v2y = 8.5*sin53

from momentum conservation

along x axis

total momentum is conserved

initial momentum = final momentum

Pix = Pfx

m1*u1x + m2*u2x = m1*v1x + m2*v2x

65*0 + 45*12 = (65*v1x)+ (45*8.5*cos53)

v1x = 4.8 m/s <<-------answer

along y

Piy = Pfy

m1*u1y + m2*u2y = m1*v1y + m2*v2y

0 + 45*0 = (65*v1y)+(45*8.5*sin53)

v1y = -4.7 m/s <<------answer

1)

magnitude = v1 = sqrt(v1x^2+v1y^2)

v1 = sqrt(4.8^2+4.7^2) = 6.72 m/s

+++++++++++++++++++

2)

direction

tan^-1(v1y/v1x) = -44.4 degrees