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Projectile Motion given only distances

  1. Jan 26, 2012 #1
    1. The problem statement, all variables and given/known data
    Standing on the ground 3.5 m from the wall of a building, you want to throw a package from your 1.6 m shoulder level to someone in a second-floor window 4.5 m above the ground. At what speed should you throw the package so it just barely reaches the window? At what angle should you throw the package so it just barely reaches the window?


    2. Relevant equations
    I looked through all my lecture notes, the book and several websites trying to find some equations that would allow me to solve this but all of them required at least one of the variables that were not given.

    vy = v0sinθ0 - gt
    y = v0sinθ0t - (1/2)gt2.
    x = v0xt
    y = xtan(θ0) - gx2/(2v02cos20))

    I'm sure I'm missing a few but I don't know which would be needed, hence the post.


    3. The attempt at a solution

    I tried using trig to find the angle. I got 39.6442° which was incorrect according to the website, so I am stumped.
     
  2. jcsd
  3. Jan 26, 2012 #2
    You solve this with using the equations of motion.

    Break the problem up into solving for the y-direction and then the x-direction.

    You know the acceleration, g, in the vertical direction, the distance in the vertical direction, and the velocity of the package just to reach the window height would be what ??
    From those facts you can calculate the vertical velocity of the package as it leaves your hand.

    Here are some equations from a site:
    http://hyperphysics.phy-astr.gsu.edu/hbase/mot.html#mot1

    ( You should familiarize yourself with them, so you don't have to look them up all the time )

    Then you can solve for the velocity in the x-direction, for the ball to reach the window horizontally.

    From the vertical and horizontal velocities you can then calculate the speed and angle of the package.
     
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