Question

You and your friends are doing physics experiments on a frozen pond that serves as a frictionless, horizontal surface. Sam, with mass 70.0kg , is given a push and slides eastward. Abigail, with mass 59.0kg , is sent sliding northward. They collide, and after the collision Sam is moving at 36.0? north of east with a speed of 7.00m/s and Abigail is moving at 21.0? south of east with a speed of 8.60m/s .

A) What was the speed of each person before the collision?
Sam's speed? ---12.4

B) Abigail's speed? --- i need help, I got 7.96 but it is wrong apparently

C) By how much did the total kinetic energy of the two people decrease during the collision?

Answer 1

Total momentum along x axis or towards east after collision = (70*7*cos 36) + (59*8.6*cos 21)
= 870.12 = 70*u or required initial speed of Sam = 12.43 m/s
Total momentum along y axis or towards north after collision = (70*7*sin 36) - (59*8.6*sin 21)
= 106.17 = 59*v or required initial speed of Abigail = 1.8 m/s

Sam's KE before the collision is 0.5*70*12.43^2 = 5407.67J
Sam's KE after the collision is 0.5*70*7^2 = 1715
Abigail's KE before the collision is 0.5*59*1.8^2 = 95.58J
Abigail's KE after the collision is 0.5*59*8.60^2 = 2181.82
The total KE lost in the collision is 1606.43J