Two ice skaters, Daniel (mass 70.6 kg) and Rebecca (mass 50.2 kg) are practicing

Question

Two ice skaters, Daniel (mass 70.6 kg) and Rebecca (mass 50.2 kg) are practicing. Daniel stops to tie his shoelace and, while at rest, is struck by Rebecca, who is moving at 12.5 m/s before she collides with him. After the collision, Rebecca has a velocity of magnitude 6.8 m/s at an angle of 52.3° 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

a)

let the final speed of daniel is v

Now , using conservation of momentum in initial direction

vx * 70.6 + 50.2 * 6.8 * cos(52.3) = 50.2 * 12.5

solving for vx

vx = 5.93 m/s

using conservation of momentum in perpendicular dircetion

vy * 70.6 + 50.2 * 6.8 * sin(52.3) = 0

vy = -3.826 m/s

Now , magnitude of daniel's speed = sqrt(5.93^2 + 3.826^2)

magnitude of daniel's speed = 7.06 m/s

direction = arctan(-3.826/5.93)

direction = -32.8 degree

velocity of daniel is 7.06 m/s at -32.8 degree below initial direction

b)

Change in total kinetic energy = final kinetic energy - initial kinetic energy

Change in total kinetic energy = 0.5 * 50.2 * 6.8^2 + 0.5 * 70.6 * 7.06^2 - 0.5 * 50.2 * 12.5^2

Change in total kinetic energy = -1002 J

the Change in total kinetic energy is -1002 J

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