Physics High School









34. (I) A novice skier, starting from rest, slides down a fric- tionless 35.0° incline whose vertical height is 185 m. How fast is she going when she reaches the bottom?

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Answer 1

A novice skier, starting from rest, slides down a fric- tionless 35.0° incline whose vertical height is 185 m, she going when she reaches the bottom with final speed is 45.8 m/s.

When a novice skier begins to slide down a frictionless 35.0° incline whose vertical height is 185 m, her initial velocity is zero. Since the incline is frictionless, the net force acting on the skier is the gravitational force. The gravitational potential energy of the skier decreases as she moves down the incline, while her kinetic energy increases until she reaches the bottom of the incline. At the bottom of the incline, the skier has converted all of her initial gravitational potential energy into kinetic energy. Using the principle of conservation of energy, we can find her final speed by equating the initial potential energy with the final kinetic energy.

Writing down the expression for conservation of energy, we get:mg * h = (1/2) * m * v²

Where, m is the mass of the skier, g is acceleration due to gravity, h is the height of the incline, and v is the final velocity we want to find out.

Substituting the given values in the expression we get:v = √(2 * g * h * sin θ)

So, the skier reaches the bottom of the incline with a speed of √(2 * 9.81 m/s² * 185 m * sin 35.0°) = 45.8 m/s.

Therefore, when the novice skier slides down a frictionless 35.0° incline whose vertical height is 185 m, her final speed is 45.8 m/s.

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