# Find distance from ramp at which skier lands

• MickeyBlue
In summary, the skier leaves the ramp of a ski jump with an initial velocity of 10.0 m/s at 15° above the horizontal. The slope of the mountain below the ramp is 50° and air resistance is negligible. Using the equations sf = si + vist + ½ast2, tanΘ = y(t)/x(t), Vix = VicosΘ, and Viy = VisinΘ, the distance from the end of the ramp at which the skier lands is 27.8m along the slope of the mountain. This was found by setting up an equation using displacements as a function of time and using trigonometry to find the final horizontal distance travelled.
MickeyBlue

## Homework Statement

A skier leaves the ramp of a ski jump with V=10.0 m/s at 15° above the horizontal. Slope of mountain below ramp is 50°. Assuming air resistance is negligible, find distance from end of ramp at which skier lands.

## Homework Equations

1. sf = si + vist + ½ast2
2. tanΘ = y(t)/x(t)
3. Vix = VicosΘ
4. Viy = VisinΘ

## The Attempt at a Solution

See attachment below. I'm fairly confident in my working yet I know 27.8m isn't correct. I'm having difficulty finding my mistake though. I'm hoping someone else is more eagle-eyed.

It's exceedingly difficult to make out the details of your work in your attached image. You'll have to do something about that if you want others to help.

MickeyBlue said:
find distance from end of ramp at which skier lands.
You mean the distance between take off point and landing point "along the slope of mountain"?
It is not 27.8m. It is hard to follow your working. Set up an equation using displacements as a function of time and a little trigonometry.

Sorry about that; it looked clearer from my side.

MickeyBlue said:
Sorry about that; it looked clearer from my side. View attachment 105255
Looks good! Xf is the horizontal distance travelled. I thought the problem was asking for the distance along the slope. I think your answer is correct.

cnh1995, you're right. I misinterpreted the question. It should have been the distance along the slope.

MickeyBlue said:
It should have been the distance along the slope.
Then you can get it using simple trigonometry now that you have Xf.

I got the final answer. Thank you very much.

## 1. How is the distance from the ramp calculated for a skier's landing?

The distance from the ramp is calculated using the equations of motion, specifically the horizontal displacement equation: d = v0t + 1/2at2. This equation takes into account the initial velocity (v0), the acceleration due to gravity (a = 9.8 m/s2), and the time (t) that the skier spends in the air.

## 2. What factors affect the distance a skier travels from the ramp?

The distance a skier travels from the ramp is affected by a few key factors: the initial velocity, the angle of the ramp, air resistance, and the slope of the landing surface. A higher initial velocity or a steeper ramp will result in a longer distance, while air resistance and a flatter landing slope will decrease the distance.

## 3. Can the distance from the ramp be determined for any type of ramp or slope?

Yes, the distance from the ramp can be calculated for any type of ramp or slope as long as the necessary information is known, such as the initial velocity, ramp angle, and landing slope. However, the equations used may differ slightly depending on the specific situation.

## 4. Is the distance traveled from the ramp the same as the horizontal distance traveled by the skier?

No, the distance traveled from the ramp is not the same as the horizontal distance traveled by the skier. The horizontal distance traveled by the skier takes into account the curvature of the landing slope, while the distance from the ramp only considers the horizontal distance from the starting point to the point of landing.

## 5. Are there any other factors that may affect the distance a skier lands from the ramp?

Yes, there are other factors that may affect the distance a skier lands from the ramp. These can include wind speed and direction, snow conditions, and the skier's technique and body position during the jump. These factors may not be as significant as the main factors mentioned earlier, but they can still have an impact on the distance traveled.

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