Solving a Skier's Horizontal Distance Problem

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In summary, a skier is starting from rest at the top of a 10.5 degree inclined hill with a coefficient of friction of 0.075. The hill is 200m long and at the bottom, the snow is level with the same coefficient of friction. The skier wants to know how far they will travel along the horizontal portion of the snow before coming to rest. All necessary equations are provided and with the given information, the problem can be solved using components and one equation.
  • #1
A PP4L K
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Homework Statement



A skier starts from rest at the top of a hill that is inclined at 10.5degrees with the horizontal. The hillside is 200 m long, and the coefficient of friction between the skis is 0.075. At the bottom of the hill, the snow is level and the coefficient of friction is unchanged. How far does the skier move along the horizontal portion of the snow before coming to rest?


Homework Equations


Ff=μFnorm
Fnet=ma
cosθ=adj/hyp
sinθ=opp/adj
tanθ=opp/adj


The Attempt at a Solution


μ = .075
d = 200m
incline = 10.5°

I know I must use components to solve, but the way this problem is set up (lack of givens) I am having trouble solving it. Also I do not know how to calculate it once he hits horizontal land and is no longer on the slope. A walk-through of this would be absolutely AMAZING! :)
 
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  • #2


A PP4L K said:

Homework Statement



A skier starts from rest at the top of a hill that is inclined at 10.5degrees with the horizontal. The hillside is 200 m long, and the coefficient of friction between the skis is 0.075. At the bottom of the hill, the snow is level and the coefficient of friction is unchanged. How far does the skier move along the horizontal portion of the snow before coming to rest?


Homework Equations


Ff=μFnorm
Fnet=ma
cosθ=adj/hyp
sinθ=opp/adj
tanθ=opp/adj


The Attempt at a Solution


μ = .075
d = 200m
incline = 10.5°

I know I must use components to solve, but the way this problem is set up (lack of givens) I am having trouble solving it. Also I do not know how to calculate it once he hits horizontal land and is no longer on the slope. A walk-through of this would be absolutely AMAZING! :)

You'll have to be more specific about what you think is missing from the givens. It looks okay to me.
 
  • #3


Its a very very easy question!
All data required is given. You just need one equation to solve it. Think more about it.
 

1. How do you calculate the horizontal distance a skier travels?

To calculate the horizontal distance a skier travels, you can use the formula d = v * t, where d is distance, v is velocity, and t is time. This formula assumes that the skier travels at a constant speed and in a straight line.

2. What other factors should be considered when solving a skier's horizontal distance problem?

Other factors that should be considered include the slope of the hill, wind speed and direction, and the skier's body position and technique. These factors can impact the skier's speed and trajectory, thus affecting the horizontal distance traveled.

3. Can the horizontal distance traveled by a skier be affected by the type of snow?

Yes, the type of snow can affect the horizontal distance traveled by a skier. For example, softer snow will slow down the skier, while harder, compact snow will allow the skier to travel faster and cover more ground.

4. How can you use vectors to solve a skier's horizontal distance problem?

Vectors can be used to represent the direction and magnitude of the skier's velocity. By breaking down the velocity vector into its x and y components, you can use trigonometry to calculate the horizontal distance traveled.

5. What is the role of air resistance in a skier's horizontal distance problem?

Air resistance, also known as drag, can slow down a skier's speed and decrease the horizontal distance traveled. This is because air resistance acts in the opposite direction of the skier's motion, creating a force that must be overcome. The impact of air resistance is greater at higher speeds and can be reduced by optimizing body position and equipment.

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