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 57.0 kg , is sent sliding northward. They collide, and after the collision Sam is moving at 34.0 north of east with a speed of 7.00 m/s and Abigail is moving at 25.0 south of east with a speed of 8.00 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

x direction: 80 * vS = 80*7*cos34 + 57*8*cos25 80 * vS = 80*7*0.8290376 + 57*8*0.90630779 v_Sam = 10.9692 m/s ------------------------------------------------------------ y direction: 57 * vA = 80*7*sin34 - 57*8*sin25 57 * vA = 80*7*0.559193 - 57*8*0.422618 v_Abigail = 2.11288 m/s ----------------------------------------------------------- K1-K2 = 0.5*(80)*(10.9692*10.9692-7*7) + 0.5*(57)*(8*8-2.11288*2.11288) = 4550 J ------------------------------------------------------------ Sam's speed: 11 m/s Abigail's speed: 2.11 m/s kinetic energy decrease: 4550 J

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