Two ice skaters, Daniel (mass 70.4 kg) and Rebecca (mass 49.0 kg) are practicing

Question

Two ice skaters, Daniel (mass 70.4 kg) and Rebecca (mass 49.0 kg) are practicing. Daniel stops to tie his shoelace and, while at rest, is struck by Rebecca, who is moving at 12.7m/s before she collides with him. After the collision, Rebecca has a velocity of magnitude 6.4 m/s at an angle of 55.3° from her initial direction. Both skaters move on the frictionless, horizontal surface of the rink.

(a) What are the magnitude and direction of Daniel's velocity after the collision?
_____ m/s
_____° (clockwise from Rebecca's original direction of motion)

(b) What is the change in total kinetic energy of the two skaters as a result of the collision?
_____J

Explanation / Answer

here,

mass of Daniel , md = 70.4 kg

mass of Rebecca , mr = 49 kg

initial speed of Rebecca , ur = 12.7 m/s

final speed of Rebecca , vr = 6.4 m/s

theta1 = 55.3 degree

(a)

let the velocity be vd and angle be theta2

using conservatin of momrtum along x axis

mr * ur = mr * vr*cos(theta1) + md*vd * cos(theta2)

49 * 12.7 = 49*6.4*cos(55.3) + 70.4 *vd * cos(theta2) ....(1)

using conervation of momentum along y axis

mr * vr*sin(theta1) + md*vd*sin(theta2) = 0

49 * 6.4 * sin(55.3) + 70.4 * vd* sin(theta2) = 0 ....(2)

from equation (1) and (2)

vd = 8.55 m/s

theta2 = 25.36 degree

the magnitude of velocity is 8.55 m/s
and 25.36 degree clockwise from Rebecca's original direction of motion

(b)

total kinetic energy of the two skaters as a result of the collision, KE = 0.5 * mr*ur^2 - 0.5 *(mr*vr^2 + md*vd^2 )

KE = 0.5 * 49 *12.7^2 - 0.5 * ( 49 * 6.4^2 + 70.4*8.55^2)

KE = 374.9 J

the total kinetic energy of the two skaters as a result of the collision is 374.9 J

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