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Homework Help: Calculating the trajectory of a projectile

  1. Sep 27, 2010 #1
    1. The problem statement, all variables and given/known data
    So, we have a physics project, in which we must build a water balloon launcher and launch the balloon at a stationary target about 50 yds away (normally we use meter, however we are firing on a football field). I have created my launcher (it is basically a slingshot), but now I must find certain aspects of the trajectory. I must find:
    (a) Initial Velocity
    (b) Maximum height
    (c) Angle of Launch


    2. Relevant equations
    v = vo+at
    x = xo+vot+(1/2)at2
    v2 = vo2+2a(x-xo)
    Range = v02sin2θ/g


    3. The attempt at a solution
    So, I know that my distance is 50 yds. I know my angle is 45o, because 45o is the degree at which one gets the most effective range. Now, for my time, I have not yet actually calculated it, so lets just say it's... 1.78 s (does that sound reasonable?). I am pretty sure that given this information, it shouldn't be too difficult for me to find my unknowns.
    I'll attempt to start by finding the initial velocity... Now, initial velocity, I know, is quite a bit different from my average velocity (total distance/total time). So... I know that in the vertical direction, the velocity is affected by gravity, and (disregarding air resistance and such), there is no positive or negative velocity in the horizontal direction. I do have my angle. So, there is VoSin/Cos(theta)= Voy/ox. Umm.... now I am a bit stuck...
    Once I find the initial velocity, finding the maximum shouldn't be too hard, however I still may need a bit of help with it...

    Or, perhaps Range = v0y2sin2θ/g
    Range = 50 yd
    v0y = ?
    θ = 45
    Ah, so that may work...
    So, v0y=Square root((Range*g)/(Sin2θ))
    So, v0y=Square root(( 45.72m*9.81m/s^2)/(Sin2(45))
    So, v0y=22.40 m/s = 24.49 yd/s
    Okay, so that's the initial velocity in the y direction. Progress.

    So, VoSin(theta)= Voy Then:
    Vo=?
    theta=45
    Voy=22.40 m/s
    So then, Vo=26.32m/s. Awesome, found it. Still would like to make sure it's correct, so I will continue to post this.

    So, now maximum height. I think I will go with v2= vo2+2a(s-so), using the y component.
    v=0 (since the velocity in the y direction at max height is 0 )
    v0y=22.40 m/s
    a=-g
    s=?
    s0=0
    SO, set up to solve for x... So, (-Vo^2)/(-2g). So, x=25.57m
    Is that correct? If so, awesome. Thanks for all the help! haha.
     
  2. jcsd
  3. Sep 27, 2010 #2
    *bump* so could someone just confirm that I did this correctly? Please? This is due tomorrow....
     
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