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 79.0 , is given a push and slides eastward. Abigail, with mass 57.0 , is sent sliding northward. They collide, and after the collision Sam is moving at 40.0 north of east with a speed of 5.60 and Abigail is moving at 15.0 south of east with a speed of 8.00 .
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

According to conservation of momentum along the x axis (sam momentum before and after collision)       (79) Vi + 0 = (79) (5.6) cos 40 + (57) (8) cos 15           Vis = 9.87m/s          According to conservation of momentum along the x axis (abigail momentum before and after collision)        0 + (57) Via = (79) (5.6) sin 40 - (57) (8) sin 15           Via = 2.92m/s According to conservation of momentum along the x axis (abigail momentum before and after collision)        0 + (57) Via = (79) (5.6) sin 40 - (57) (8) sin 15           Via = 2.92m/s       The initial kinetic energy        = (1/2)(79)(9.87)^2 + (1/2)(57)(2.92)^2        = 4090.96 J Final speed       = (1/2) (79)(5.6)^2 + (1/2)(57)(8)^2       = 3062.72 J Change in KE      = 4090.96 - 3062.72      = 1028.2 J

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