Question

Two ice skaters, Daniel (mass 65 kg) and Rebecca (mass 45 kg), are practicing. Daniel stops to tie his skate lace and, while at rest, is struck by Rebecca who is moving at 13.0 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. 1) Determine the magnitude of the x-component Daniel's velocity after the collision. 2) Determine the magnitude of the y-component Daniel's velocity after the collision.

Answer 1

m1 (daniel) = 65 kg       m2 ( Rebecca) = 45 kg

u1x = 0               u2x = 13 m/s

U1y = 0               u2y = 0

after collision

v1x = ?               v2x = v2*cos53.1 = 8*cos53.1

v1y = ?               v2y = v2*sin53.1 = 8*sin53.1

total momentum is conserved

along x axis

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

(65*0) + (45*13) = (65*v1x) + (45*8*cos53.1)

v1x = 5.67 m/s <<<<----------answer

along y axis

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

(65*0) + (45*0) = (65*v1y) + (45*8*sin53.1)

v1y = -4.43 m/s

magnitude of y component v1y = 4.43 m/s <<<<----------answer