How Do You Calculate Snow Projection Components on a Slope?

[BeckyStar678]

Homework Statement

a snow-covered ski slope makes an angle of 35 degrees with the horizontal. when a ski jumper plummets onto the hill, a parcel of splashed snow projects to a maximum position of 5 m at 20 degrees from the vertical in the uphill direction. find the components of its maximum position a.) parallel to the surface and b.) perpendicular to the surface.

Homework Equations

The Attempt at a Solution

would i just use a triangle with 20 degrees and 5 meters as the hypotenuse. then find the other two sides using trig and those two sides i find are the parallel and perpendicular sides

 

[tiny-tim]

Hi BeckyStar678!

would i just use a triangle with 20 degrees and 5 meters as the hypotenuse. then find the other two sides using trig and those two sides i find are the parallel and perpendicular sides

No … that would give you the components parallel and perpendicular to the ground.

Hint: you need to draw a right-angled triangle with sides parallel and perpendicular to the slope.

 

[baba89]

to the surface?

Yes, you are correct. You can use trigonometry to find the components of the maximum position. The 5 meters acts as the hypotenuse of the triangle, and the angle of 20 degrees represents one of the acute angles. Using trigonometric ratios, you can find the lengths of the sides of the triangle, which would give you the components of the maximum position parallel and perpendicular to the surface.