Find distance from ramp at which skier lands

[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 + vi_st + ½a_st²
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.

 

[gneill]

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.

 

[cnh1995]

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.

 

[MickeyBlue]

Sorry about that; it looked clearer from my side.

 

[cnh1995]

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.

 

[MickeyBlue]

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

 

[cnh1995]

It should have been the distance along the slope.

Then you can get it using simple trigonometry now that you have Xf.

 

[MickeyBlue]

I got the final answer. Thank you very much.