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?

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