Two ice skaters, Daniel (mass 69.2 kg) and Rebecca(mass 50.8 kg) are practicing,

Question

Two ice skaters, Daniel (mass 69.2 kg) and Rebecca(mass 50.8 kg) are practicing, Daniel stops to tie his shoelace and, while at rest, is struck by Rebecca, who is moving at 13.2 m/s before she collides with him. After the collision, Rebecca has a velocity of magnitude 6.3 m/s at an angle of 53.7 degree from her initial direction. Both skaters move on the frictionless, horizontal surface of the rink. What are the magnitude and direction of Daniel's velocity after the collision? What is the change in total kinetic energy of the two skaters as a result of the collision?

Explanation / Answer

here,

let the initial motion be in + x direction

m1 = 69.2 kg

m2 = 50.8 kg

initial speed of Rebecca , u2 = 13.2 i m/s

final speed of Rebecca , u2 = 6.3 * ( cos(53.7) i + sin(53.7 ) j) m/s

v2 = 3.73 i m/s + 5.08 j m/s

let the final speed of Daniel be v1

m1 * u1 + m2 * u2 = m1 * v1 + m2 * v2

50.8 * 13.2 i = 69.2 * v1 + 50.8 * (3.73 i m/s + 5.08 j m/s )

v1 = (6.95 i - 3.73 j ) m/s

|v1| = sqrt(6.95^2 + 3.73^2)

|v1| = 7.89 m/s

direction , theta = arctan(3.73 /6.95) = 28.2 degre from the initial direction

b_)

the change in kinetic energy , KE = 0.5 * m1 * v1^2 + 0.5 * m2 * v2^2 - 0.5 * m2 * u2^2

KE = 0.5 * ( 69.2 * 7.89^2 + 50.8 * 6.3^2 - 50.8 * 13.2^2) J

KE = - 1.26 * 10^3 J

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