Two ice skaters, Daniel (mass 70.0 kg ) and Rebecca (mass 45.0 kg ), are practic

Question

Two ice skaters, Daniel (mass 70.0 kg ) and Rebecca (mass 45.0 kg ), are practicing. Daniel stops to tie his shoelace and, while at rest, is struck by Rebecca, who is moving at 14.0 m/s before she collides with him. After the collision, Rebecca has a velocity of magnitude 7.00 m/s at an angle of 55.1 from her initial direction. Both skaters move on the frictionless, horizontal surface of the rink.

1- What is the magnitude of Daniel's velocity after the collision?

2- What is the direction of Daniel's velocity after the collision?

3- What is the change in total kinetic energy of the two skaters as a result of the collision?

Explanation / Answer

initially daniel at rest , and rebecca has 14 m/s in horizontal = 14 m/s

after collision rebecca horizontal component of velocity = vr2x = 7 *cos55.1 = 4 m/s

in vertical component = 5.74 m/s

now momentum is conserve

in x direction

mrvr1x = mrv2x + md*vd2x

vd2x = 45 * (14 - 4) / 70

vd2x = 6.42857

in y direction

initially both do not have any component in y direction

0 = mr*vr2y + md*vd2y

vd2y = -3.69 m/s

vd2 = sqrt(vd2x^2 + vd2y^2)

vd2 = 7.41 m/s

parrt 2 )

theta = tan^-1(vd2y/vd2x)

theta = 29.86 degree below +x

part 3 )

K1 = danies at rest

K1 = 1/2*mr*vr1^2 = 4410J

K2 = 1/2*md*vd2^2 + 1/2*mr*vr2^2

K2 = 3024.2835 J

dK = K2- K1 = -1385.7165 J

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