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Kinematics help

  1. Jun 15, 2008 #1
    a tank shoots at a target on a mountain 10km away from it, the hight of the mountain is 500m the tank shoots at a speed of 1800km/h, at which angles can the tank aim?

    this is a question in kinematics and the only force to take into account is gravity,


    using
    V(t)=Vo+at
    X(t)=Xo+Vot+½at²
    V²-Vo²=2aΔx

    Vx=const=cosθ*Vo
    Vy(t)=sinθ*Vo+at

    Vo=500m/s
    Xf=10000m
    Yf=500m

    knowing that the target is at (10000,500) i use the equation for X,
    X(tf)=500cosθ*tf=10000m
    tf=20/cosθ

    Y(tf)=500m=500sinθ*(20/cosθ)-4.9*(20/cosθ)²
    =1000tanθ-1960/(cosθ)²


    now from here i dont know what to do, one equation with both tanθ and cosθ, how do i bring them to some common expression?? i have had a very similar quesion before which i too could not get past this point.

    since i do not have T, i thought of using the 3rrd equation, but i dont see how i can
     
  2. jcsd
  3. Jun 15, 2008 #2

    Defennder

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    Homework Helper

    Instead of solving in terms of theta, why not try solving in terms of t first?
     
  4. Jun 15, 2008 #3
    how would you do that
     
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