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Projectile motion problem

  1. Nov 28, 2008 #1
    Projectile motion problem - SOLVED

    1. The problem statement, all variables and given/known data
    This is one of the last parts of a bigger problem, but I get the first parts. So:

    The projectile motion describes a skier's jump. The initial velocity is 21.469m/s at 20 degrees to the horizontal. Find the maximum height the skier reaches (relative to the take off point), find distance 'd' down the slope where the skier lands.

    3. The attempt at a solution
    First I wrote the equations:
    Vx = 21.469cos(20)
    Vy= 21.469sin(20)-gt

    Then, I found the time it took for the skier to reach the top:
    t= 0.7485 seconds

    Then I found the 'h':
    ds/dt = 21.469sin(20)-9.81t
    s(0.7485) = 2.7481 m

    Then I drew this:
    On it, I calculated the 30.2 value by plugging in 0.7485*2 into an x-direction distance equation:
    Sx = 0.7485*2 x 21.469cos20 = 30.2
    I then found the 17.44 using just trig.

    So now, I started to treat the big triangle (described by p and q) as a similar triangle with sides 30.2&17.44 and developed a relationship:
    q/p = 17.44/30.2

    Next, I expressed d in terms of p and q:
    d2= 1.3329p2
    and thus, p=0.866d
    I performed similar operations and got:

    Then time for the skier to go the whole horizontal distance:
    0.886d = 21.469cos(20)*t
    And thus the time it will take for the skier to hit the ground from her highest point is:

    Now, we can plug in that equation into the equation of vertical distance travelled:
    h+0.5d = 21.469sin(20)(0.0429d-0.7485)-4.905(0.04293d-0.7485)2
    I can simplify that and try to find d (from discriminant and things) but I end up with a negative discriminant... Help?
    Last edited: Nov 28, 2008
  2. jcsd
  3. Nov 28, 2008 #2


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    Homework Helper

    You might be better served to solve it more simply.

    y = Vy*t - 1/2*g*t2

    And because of the slope y = -x*tan30

    and x = Vx*t

    Where y intersects with the slope is where he lands.

    -Vx*t*tan30 = Vy*t - 1/2*g*t2

    Solve for t and plug it into either equation.
  4. Nov 28, 2008 #3
    Wow, thanks! That's so much easier and makes a lot more sense! :)
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