A skier starts from rest at the top of a hill that is inclined at 9.8° with the horizontal. The hillside is 170 m long, and the coefficient of friction between snow and skis is 0.0750. At the bottom of the hill, the snow is level and the coefficient of friction is unchanged. How far does the skier glide along the horizontal portion of the snow before coming to rest?
during the slide down the hill:
use a=gSin9.8-mu*gCos9.8 to find vel. at the base of the incline. For the horizontal part accleration is -mu*g - to find the distance covered.
Figure it out based on the above hint
To find the distance the skier glides along the horizontal portion of the snow before coming to rest, we can break down the problem into two parts:
1. Finding the skier's velocity at the bottom of the hill.
2. Using the skier's velocity to determine the distance traveled along the horizontal portion of the snow.
Part 1: Finding the skier's velocity at the bottom of the hill
The skier's initial velocity at the top of the hill is 0 since they start from rest. We can find the skier's final velocity at the bottom of the hill using the conservation of energy:
Potential Energy at the top of the hill = Kinetic Energy at the bottom of the hill
The potential energy at the top of the hill can be calculated using the formula:
Potential Energy = mass * acceleration due to gravity * height
Since the skier is on an inclined plane, the height can be calculated using the formula:
Height = hillside length * sin(theta)
where theta is the angle of inclination (9.8°) converted to radians.
The kinetic energy at the bottom of the hill can be calculated using the formula:
Kinetic Energy = (1/2) * mass * (velocity)^2
Now, by equating the potential energy to the kinetic energy and solving for velocity, we can find the skier's velocity at the bottom of the hill.
Part 2: Determining the distance traveled along the horizontal portion of the snow
Once we have the skier's velocity at the bottom of the hill, we can determine the distance traveled along the horizontal portion of the snow using the equation of motion:
Distance = (Velocity^2) / (2 * acceleration)
where the acceleration is the frictional force acting on the skier, which can be calculated using the formula:
Frictional Force = coefficient of friction * Normal Force
The normal force acting on the skier is equal to the skier's weight since there is no vertical acceleration:
Normal Force = mass * acceleration due to gravity
Now that we have the frictional force, we can calculate the skier's acceleration using Newton's second law of motion:
Acceleration = Frictional Force / mass
Finally, using the skier's velocity and acceleration, we can calculate the distance traveled along the horizontal portion of the snow.
Therefore, to find the distance the skier glides along the horizontal portion of the snow before coming to rest, apply the above steps and calculations.