You and your friends are doing physics experiments on a frozen pond that serves as a frictionless, horizontal surface. Sofia, with mass 78.0 kg , is given a push and slides eastward. Elena, with mass 52.0 kg , is sent sliding northward. They collide, and after the collision Sofia is moving at 32.0 ∘∘ north of east with a speed of 6.20 m/s and Elena is moving at 19.0 ∘∘ south of east with a speed of 9.40 m/s .  By how much did the total kinetic energy of the two people decrease during the collision?

The eight ball, which has a mass of m = 0.5 kg, is initially moving with a velocity v = 4.7i m/s. It strikes the six ball inelastically, which has an identical mass and is initially at rest. After the collision the eight ball is deflected by an angle of θ = 19° and the six ball is deflected by an angle of Φ = 13°, as shown in the figure.   a. Write an expression for the magnitude of six ball's velocity, in terms of the angles given in the problem and the magnitude of the eight ball's initial velocity, v.   (b)  What is the magnitude of the velocity, in meters per second, of the six ball?   (c)  What is the magnitude of the velocity of the eight ball, in meters per second, after the collision?

In the figure, mass m1=10.0 kg is moving at a speed of Vi1 undergoes a collision with mass m2 = 7.00 kg with speed Vi2 at θi = 37°. After the collision, the two masses stick together and keep moving with Vf at θf = 17°. The change in kinetic energy ∆K = −58.5 J, What is the velocity before the collision of Vi1 and Vi2 and after the collision of Vf?

An 87 kg wide receiver is running at 9.4 m/s and is hit by a 110 kg linebacker traveling in the opposite direction. After the collision, the two players move together in the receiver’s original direction at a speed of 1.6 m/s. How fast was the linebacker moving before the collision?