A skier starts from rest at the top of a hill that is inclined at 9.5° with respect to the horizontal. The hillside is 225 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?

m

Why did the skier bring a tape measure to the hill? They wanted to measure the "slippery slope" of physics!

Anyway, let's get calculating. To find out how far the skier glides along the horizontal portion of the snow, we need to first determine the velocity the skier reaches at the bottom of the hill.

Using energy conservation, we can determine the velocity of the skier at the bottom of the hill using the formula:

v = sqrt(2gh)

where v is the velocity, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height of the hill (which can be calculated as 225 m * sin(9.5°)).

Once we determine the velocity, we can calculate the distance the skier glides along the horizontal portion of the snow using the formula:

d = (v^2) / (2 * μ * g)

where d is the distance, v is the velocity, μ is the coefficient of friction, and g is the acceleration due to gravity.

Now, let's plug in the numbers and solve! Just remember, I'm here to make you smile, not to slide down the hill myself!

Calculating... calculating...

The skier glides along the horizontal portion of the snow for approximately [insert calculated distance] meters. Good luck catching them!

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 different steps:

Step 1: Find the initial velocity of the skier at the bottom of the hill.
Given:
- The skier starts from rest (meaning initial velocity, v0 = 0).
- The hill is inclined at an angle of 9.5° with respect to the horizontal.

To determine the initial velocity of the skier at the bottom of the hill, we can use the equation of motion: v = v0 + at, where v is the final velocity, v0 is the initial velocity, a is the acceleration, and t is the time taken.

Since the hill is inclined, the acceleration acting on the skier will be due to the component of the gravitational force acting down the incline. This acceleration can be calculated using the formula: a = g * sin(θ), where g is the acceleration due to gravity (9.8 m/s²) and θ is the angle of the incline (9.5°).

a = g * sin(θ)
a = 9.8 m/s² * sin(9.5°)
a ≈ 1.60 m/s²

Using the equation v = v0 + at and plugging in the values, we have:
0 + a * t = v
t = v / a

Since we are trying to find the distance traveled along the horizontal portion of the snow before coming to rest, we can ignore the vertical component and only consider the horizontal component of the velocity.

Step 2: Find the time taken to reach the horizontal portion of the snow.
Given:
- The hillside is 225 m long.

To find the time taken, we can use the equation of motion: s = v0 * t + 1/2 * a * t², where s is the distance traveled, v0 is the initial velocity, a is the acceleration, and t is the time taken.

Since the skier starts from rest at the top of the hill, the initial velocity is 0. The distance traveled can be determined using the length of the hillside (225 m).

s = v0 * t + 1/2 * a * t²
225 m = 0 * t + 1/2 * a * t²
225 m = 1/2 * a * t²
t² = (225 m) * 2 / a
t = sqrt[(225 m) * 2 / a]

Plugging in the values, we have:
t = sqrt[(225 m) * 2 / 1.60 m/s²]
t ≈ 10.54 s

Step 3: Find the distance traveled along the horizontal portion of the snow.
Given:
- The coefficient of friction between snow and skis is 0.0750.

To find the distance traveled, we can use the equation of motion: s = v * t, where s is the distance traveled, v is the final velocity, and t is the time taken.

The final velocity can be calculated using the equation v = v0 + at.

v = v0 + at
v = 0 + a * t
v = a * t

Plugging in the values, we have:
v = 1.60 m/s² * 10.54 s
v ≈ 16.86 m/s

Now, we can find the distance traveled along the horizontal portion of the snow using the equation s = v * t.

s = 16.86 m/s * 10.54 s
s ≈ 177.79 m

Therefore, the skier glides along the horizontal portion of the snow for approximately 177.79 meters before coming to rest.

To find out how far the skier glides along the horizontal portion of the snow, we need to calculate the distance using the given information.

First, let's find the component of the gravitational force parallel to the hill. The total force acting on the skier along the hill can be calculated using the formula:

Force = mass * acceleration
Since the skier is at rest initially, the acceleration can be calculated using the formula:

acceleration = gravity * sin(θ)
where θ is the angle of inclination of the hill (9.5°) and gravity is the acceleration due to gravity (9.8 m/s^2).

Plugging in the values, we get:
acceleration = 9.8 * sin(9.5°)

Now, we can calculate the force parallel to the hill:
Force_parallel = mass * acceleration

Given that the coefficient of friction between the snow and skis is 0.0750, we can calculate the frictional force using the formula:

Frictional force = coefficient of friction * normal force
Since the skier is on a slope, the normal force can be calculated as:

Normal force = mass * gravity * cos(θ)

Plugging in the values, we get:
Normal force = mass * 9.8 * cos(9.5°)

Now, we can calculate the frictional force:
Frictional force = 0.0750 * Normal force

Since the frictional force acts against the force along the hill, the net force can be calculated as:
Net force = Force_parallel - Frictional force

Once we have the net force, we can calculate the acceleration along the horizontal portion of the snow. Since the skier comes to rest, the final velocity is 0 m/s. Using the equation of motion:

Final velocity^2 = Initial velocity^2 + 2 * acceleration * distance
0 = Initial velocity^2 + 2 * acceleration * distance
Since the skier starts from rest, the initial velocity is 0 m/s. Thus, the equation becomes:
0 = 0 + 2 * acceleration * distance
0 = 2 * acceleration * distance

Rearranging the equation, we get:
distance = 0 / (2 * acceleration)

Now, we can substitute the values and calculate the distance:
distance = 0 / (2 * acceleration)

After calculating this expression, you will find that the distance is zero. This means the skier does not glide along the horizontal portion of the snow before coming to rest.

h = 225*sin9.5 = 37.1 m. = Ht. of hill.

V^2 = Vo^2 + 2g*d.
V^2 = 0 + 19.6*37.1 = 727.2
V = 27 m/s. = Skier,s velocity at bottom
of hill.

u = -a/g = 0.075.
-a/9.8 = 0.075
a = -0.735 m/s^2. = Acceleration of skier.

d = (V^2-Vo^2)/2a.
d = (0-(27)^2)/-1.47 = 496 m.