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Stone on Roof, Find Distance

  1. Oct 6, 2013 #1
    1. The problem statement, all variables and given/known data
    We are standing at a distance d=15 m away from a house. The house wall is h=6 m high and the roof has an inclination angle β=30 ∘. We throw a stone with initial speed v0=20 m/s at an angle α= 44 ∘. The gravitational acceleration is g=10 m/s2. (See figure)

    (a) At what horizontal distance from the house wall is the stone going to hit the roof - s in the figure-? (in meters)

    (b) What time does it take the stone to reach the roof? (in seconds)

    2. Relevant equations



    3. The attempt at a solution
    I set up 2 equations :
    s+15=20*cos(44)*t
    s/sqrt(3)+6=20*sin(44)*t-5t^2
    and got s=.99 and t=1.11. What did I do wrong?
     

    Attached Files:

  2. jcsd
  3. Oct 6, 2013 #2

    Simon Bridge

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    How did you arrive at those equations?
    (Please show your reasoning.)
    How did you account for the slope of the roof?
     
  4. Oct 6, 2013 #3
    I used the equation x=v_0*t+.5*a*t^2. I created a 30-60-90 triangle , and realized that for each distance s horizontally it goes up by s/sqrt(3). The total distance horizontally is 15+s and vertically is (s/sqrt(3)_6) and we are given the acceleration and launch velocity/angle.
     
  5. Oct 7, 2013 #4

    Simon Bridge

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    As a description, that leaves a lot to be desired.

    You need to know where the trajectory parabola of the stone intersects the line of the roof.
    What is your strategy for figuring that out?
     
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