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 70.0 kg , is given a push and slides eastward. Abigail, with mass 59.0 kg , is sent sliding northward. They collide, and after the collision Sam is moving at 37.0 north of east with a speed of 6.00 m/s and Abigail is moving at 19.0 south of east with a speed of 10.0 m/s . Part A: What was the speed of each person before the collision? Sam's speed: Part B: Abigail's speed: Part C: By how much did the total kinetic energy of the two people decrease during the collision?

Explanation / Answer

Vis = initial velocity of sam in east direction

Via = initial velocity of abigail in north direction

Using conservation of momentum along east -west direction

ms Vis + ma (0) = ms (6 Cos37) + ma (10 Cos19)

70 Vis + 59 (0) = 70 (6 Cos37) + 59 (10 Cos19)

Vis = 12.8 m/s

Using conservation of momentum along north-south direction

ms (0) + ma Vai = ms (6 Sin37) + ma (- 10 Sin19)

70 (0) + 59 Vai = 70 (6 Sin37) + 59 (- 10 Sin19)

Vai = 1.03 m/s

initial Total KE = (0.5) [ms V2is + ma V2ai ] = (0.5) [70 (12.8)2 + 59 (1.03)2] = 5765.7 J

Final total KE = (0.5) [70 (6)2 + 59 (10)2] = 4210

decrease = final KE - initial KE = 4210 - 5765.7 = - 1555.7 J

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