Two ice skaters, Daniel (mass 69.2 kg) and Rebecca (mass 50.1 kg) are practicing

Question

Two ice skaters, Daniel (mass 69.2 kg) and Rebecca (mass 50.1 kg) are practicing. Daniel stops to tie his shoelace and, while at rest, is struck by Rebecca, who is moving at12.7 m/s before she collides with him. After the collision, Rebecca has a velocity of magnitude 6.8 m/s at an angle of 50.1° 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

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

Explanation / Answer

a) initial velocity of Daniel =   0

initial velocity of Rebecca = 12.7 m/s i

finally velocity of Rebecca vR = 6.8(cos50.1 i + sin50.1 j ) m/s

after collision suppose daniel moves with speed v at angle @ below the line of motion,

so velocity of daniel = v(cos@ i - sin@ j)

using momentum conservation,

69.2 x 0 + 50.1 x12.7 i = (50.1 x 6.8(cos50.1 i + sin50.1 j )) + (69.2v(cos@ i - sin@ j) )

along j,

50.1 x 6.8 x sin50.1   - 69.2vsin@ = 0

vsin@ = 3.78 ......(i)

along i,

50.1 x 12.7 = 50.1 x 6.8 x cos50.1   + 69.2vcos@

vcos@ = 6.04 .....(ii)

(i) / (ii)   => tan@ = 3.78 / 6.04

@ =32.04 deg ............Ans (direction)

v = 6.04 / cos32.04 =7.13 m/s .........Ans(magnitude)

b) change in KE = final KE - initial KE

     = [69.2 x 7.13^2 /2   + 50.1 x 6.8^2 /2 ] - [ 69.2x 0 +    50.1 x 12.7^2 /2 ]

      = - 1123.05 J

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