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 78.0 kg , is given a push and slides eastward. Abigail, with mass 58.0 kg , is sent sliding northward. They collide, and after the collision Sam is moving at 37.0 north of east with a speed of 7.00 m/s and Abigail is moving at 22.0 south of east with a speed of 8.80 m/s .

1- What was the speed of each person before the collision?
Sam's speed:

2- Abigail's speed:

3- By how much did the total kinetic energy of the two people decrease during the collision?

Explanation / Answer

m1 =78 kg , m2 =58 kg , u1y =0 , u2x =0

v1x = 7 cos(37) =5.59 m/s

v1y = 7 sin(37) = 4.213 m/s

v2x = 8.8 cos(22') = 8.16 m/s

v2y = - 8.8sin(22) = - 3.3 m/s

(1) From conservation of momentum along x -direction

m1u1x+m2u2x =m1v1x+m2v2x

(78*u1) +0 = (78*5.59)+(58*8.16)

u1 = 11.66m/s

(2) From conservation of momentum along y -direction

m1u1y+m2u2y =m1v1y+m2v2y

0+ (58*u2) = (78*4.213)- (58*3.3)

u2 = 2.37 m/s

(3) K1 -K2 = (1/2)m1u1^2 +(1/2)m2u2^2 -(1/2)m1v1^2 -(1/2)m2v2^2

= (0.5*78*11.66*11.66) +(0.5*58*2.37*2.37) -(0.5*78*7*7) - (0.5*58*8.8*8.8)

K1 - K2 = 1308.4 J

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