You and your friends are doing physics experiments on a frozen pond that serves

Question

You and your friends are doing physics experiments on a frozen pond that serves as a frictionless, horizontal surface. Sam, with mass 71.0 kg , is given a push and slides eastward. Abigail, with mass 60.0 kg , is sent sliding northward. They collide, and after the collision Sam is moving at 34.0 north of east with a speed of 6.20 m/s and Abigail is moving at 24.0 south of east with a speed of 9.00 m/s .
What was the speed of each person before the collision? Sam's speed? Abigail's speed?
By how much did the total kinetic energy of the two people decrease during the collision?

Explanation / Answer

the initial velocity of the first person is,

u1 = msv1 cos34 + mav2cos24 / ms = [71 * 6.2*cos34 + 60*9*cos24] / 71 = 12.08 m/s

the initial velocity of the second person is,

  u2 = msv1 sin34 - mav2sin24 / ma = [71 * 6.2*sin34 - 60*9*sin24] / 60 = 0.44 m/s

The change in kinetic energy is calculated as follows:

dK = 0.5msv12 + 0.5mav22 - 0.5msu12 - 0.5mau22

= 0.5*71*6.2*6.2 + 0.5*60*9*9 - 0.5*71*12.08*12.08 - 0.5*60*0.44*0.44

= -1391.5752 J

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