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 80.0 kg, is given a push and slides eastward. Abigail, with mass 50.0 kg, is sent sliding northward. They collide, and after the collision Sam is moving at 37.0 degree north of east with a speed of 6.00 m/s and Abigail is moving at 23.0 degree south of east with a speed of 9.00 m/s. (a) What was the speed of each person the collision? (b) By how much did the total kinetic energy of the two people decrease during the collision?

Explanation / Answer

Conserve momentum north-south and east-west.
east: 80kg * u = 80kg*6m/s*cos37 + 50kg*9m/s*cos23 = 797.5722 kg·m/s
u = 9.9696 m/s ------- Sam
north: 50kg * v = 80kg*6m/s*sin37 - 50kg*9m/s*sin23 = 113.042 kg·m/s
v = 2.26 m/s --------- Abigail

KE = 0.5*m*v^2, so before the collision the kinetic energy was:

0.5*80 kg *(9.97 m/s)^2 + 0.5*50 kg * (2.261 m/s)^2 = 4104 joules

After the collision, we have


0.5*80 kg *(6 m/s)^2 + 0.5*50 kg * (9 m/s)^2 = 3465 J

The difference (loss) in kinetic energy is 4104 - 3465 = 639 J

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