A skier of mass 50 kg is moving at speed 10 m/s at point P₁ down a ski slope with negligible friction. What is the skier's kinetic energy when she is at point P₂, 20 m below P₁? A) 2500 J B) 9800 J C) 12300 J D) 13100 J E) 15000 J

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Quizplus · Accepted Answer

The kinetic energy of the skier can be calculated by the formula KE = 1/2 mv^2, where m is the mass of the skier and v is the velocity at point P₁. KE1 = 1/2 x 50 kg x (10 m/s)^2 = 2500 J At point P₂, the skier has lost no energy due to friction, therefore the kinetic energy is conserved. We can calculate the velocity of the skier at this point using conservation of energy: PE1 + KE1 = PE2 + KE2 mgΔh + 1/2 mv^2 = mgΔh2 + 1/2 mv2^2 50 kg x 9.8 m/s^2 x (-20 m) + 2500 J = 50 kg x 9.8 m/s^2 x 0 m + 1/2 x 50 kg x v^2 v = sqrt(2 x (50 kg x 9.8 m/s^2 x 20 m + 2500 J) / 50 kg) = 28.14 m/s KE2 = 1/2 x 50 kg x (28.14 m/s)^2 = 12300 J. Therefore, the skier's kinetic energy at point P₂ is 12300 J, which corresponds to choice C.

A Skier of Mass 50 Kg Is Moving at Speed