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Super fun projectile motion ski slope problem!

  1. Oct 10, 2012 #1
    1. The problem statement, all variables and given/known data

    A ski-jumper comes off the bottom of the slope going horizontally at a speed of 20 ms. It starts off 3 m above a slope going downwards at an angle of 45 degrees. How far along the slope does it land.

    2. Relevant equations

    1) y= Vsinθ - (.5)gt^2
    2) x= Vcosθt
    3) tanβ = ||y|| / ||x||

    3. The attempt at a solution

    I attempted to find the solution by considering the beginning of the slope to be at the origin with the skiier starting 3 metres above it so my equation for y position was:

    4) y = Vsinθt - (.5)gt^2 + 3

    -which simplifies to: y = -.5gt^2 + 3 since sinθ is zero.

    The x position is given by equation 2.
    Using equation 3 to change equation 2 to give the y-position corresponding to the x-position led me to:

    -y/V = t (since Vcosθ = V in this case)

    I then used this in equation 4 to replace t, and used the quadratic formula to get an answer for the y value.

    After this step the distance is just a matter of finding the hypotenuse of a triangle and isn't of interest to me, but what I'm concerned about is that the answer I got is off slightly from what I found when I measured out the problem on computation paper and it's outside (just by a little too much) the error margins given the tools I used for drawing it.

    My question is whether or not I correctly incorporated the starting position of 3 metres above the 45 degree angle slope? Thanks :)
     
  2. jcsd
  3. Oct 11, 2012 #2

    NascentOxygen

    User Avatar

    Staff: Mentor

    That looks right. If you'd shown your working and answers I would have seen whether your answers accord with mine.
     
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