To solve this problem, we'll first determine the initial kinetic energy of the system before the cat leaps into the skier's arms, and then calculate the final kinetic energy after the cat is caught. The change in kinetic energy will give us the amount of kinetic energy converted to internal energy. We'll also find the velocity of an inertial reference frame where the cat's kinetic energy does not change.
(a) Determine the amount of kinetic energy converted to internal energy in the Earth reference frame:
The initial kinetic energy of the skier is given by the formula:
K1 = 0.5 * m_skier * v_skier^2
Where: m_skier = 60 kg (mass of the skier) v_skier = 15 m/s (velocity of the skier)
K1 = 0.5 * 60 kg * (15 m/s)^2 K1 = 0.5 * 60 kg * 225 m^2/s^2 K1 = 6750 J
The initial kinetic energy of the cat is given by:
K2 = 0.5 * m_cat * v_cat^2
Where: m_cat = 5.0 kg (mass of the cat) v_cat = -3.8 m/s (negative because the cat is moving southward)
K2 = 0.5 * 5.0 kg * (-3.8 m/s)^2 K2 = 0.5 * 5.0 kg * 14.44 m^2/s^2 K2 = 36.1 J
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