Solving Fx for 50kg Skier Down Hill

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In summary, a 50kg skier is skiing down a frictionless slope at a 16 degree angle to the horizontal with a constant velocity. A wind force with component Fx is acting on the skier. The skier's velocity is constant due to the balancing forces of -sin(16)*m*g and Fx acting in the negative x direction. However, if the skier's velocity is increasing at a rate of 10m/s/s, the equation would be -sin(16)(5)(9.8+10t).
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1MileCrash
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Homework Statement



A 50kg skier skis directly down a frictionless slope angled 16* to the horizontal. Assume the skier moves at a negative x direction. A wind force with component Fx acts on the skier.

What is Fx if the skier's velocity magnitude is constant?

Homework Equations





The Attempt at a Solution



I really have no idea. I assume Fx is equal to the force the skier exerts "on the air" so F = ma on the skier.

But I am utterly confused when they say velocity is constant. He is going down the slope due to gravity, how could his velocity be constant? It makes no sense to me.
 
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  • #2
The negative x direction is the direction the skier goes. There are two forces which act in the x direction on the skier, -sin(16)*m*g and F_x, they are equal and opposite.
 
  • #3
How would I adjust that if the skier's velocity is increasing 10m/s/s?

-sin(16)(5)(9.8 + 10t)
?
 

1. How does the weight of a skier affect their speed while skiing downhill?

The weight of a skier does not significantly affect their speed while skiing downhill. The force of gravity acting on the skier is the main factor determining their speed, not their weight. However, a heavier skier may experience slightly more resistance from the snow due to increased pressure on their skis.

2. What is the relationship between the angle of the slope and the speed of a skier?

The steeper the slope, the faster a skier will go. This is because the force of gravity acting on the skier will be greater on a steeper slope, resulting in a faster acceleration.

3. How does air resistance affect the speed of a skier?

Air resistance, also known as drag, can slow down a skier as they move downhill. This is because the air molecules push against the skier, creating a force in the opposite direction of their motion. The effect of air resistance is greater at higher speeds and can be reduced by changing the skier's position or wearing more aerodynamic gear.

4. Is there an optimal ski length for a 50kg skier going downhill?

The optimal ski length for a 50kg skier will depend on various factors such as their skill level, personal preference, and the type of terrain they will be skiing on. In general, a shorter ski length may be easier to maneuver and control, while a longer ski may provide more stability and speed.

5. How can a skier improve their speed while skiing downhill?

To improve their speed while skiing downhill, a skier can try to reduce air resistance by staying in a tucked position and wearing more aerodynamic gear. They can also practice proper technique and positioning to optimize their movements and minimize resistance. Additionally, skiing on steeper slopes with a smooth surface can also result in faster speeds.

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