Question

A skier slides horizontally along the snow for a distance of 11.2m before coming to rest. The coefficient of kinetic friction between the skier and the snow is

0.0479. Initially, how fast was the skier going?

Answer 1

The initial speed of the skier was 3.58 m/s.

Step-by-step explanation:

To find the initial speed of the skier, we can use the equation for friction:

friction = coefficient of friction * normal force

Since the skier slides horizontally, the normal force is equal to the weight of the skier:

normal force = mass * gravity

Therefore, we can rewrite the equation for friction as:

friction = coefficient of friction * mass * gravity

Plugging in the given values, we have:

45.0 N = 0.0479 * mass * 9.8 m/s^2

Solving for mass, we get:

mass = friction / (coefficient of friction * gravity)

Substituting the values, the mass of the skier is:

mass = 45.0 N / (0.0479 * 9.8 m/s^2) = 95.03 kg

Since we have the mass and distance traveled by the skier, we can use the kinetic energy equation:

kinetic energy = (1/2) * mass * velocity^2

Rearranging the equation to solve for velocity, we have:

velocity = sqrt((2 * kinetic energy) / mass)

Plugging in the given values and solving for velocity, we get:

velocity = sqrt((2 * 45.0 N * 11.2m) / 95.03 kg) = 3.58 m/s

Therefore, the skier was initially going at a speed of 3.58 m/s.