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Motion in two and three dimensions question?

  1. Jan 28, 2013 #1
    Galileo shows that, if any effects due to air resistance are ignored, the ranges for projectiles on a level field whose angles of projection exceed or fall short of 45 degrees by the same amount are equal. Prove this result.

    A: So ,I tried these vx = v*cos(q) //q is the shooting angle, vx is the speed in horizontal direction
    vy_0 = v*sin(q) //original vertical speed
    vy = vy_0 - gt // the projectile is pulled down by the gravity
    ----
    x(t) = vxt
    y(t) = vy_0t - 0.5gt^2
    ----
    when the projectile hits the ground, y is 0
    vy_0t = 0.5gt^2
    vy_0 = 0.5gt
    t = 2vy_0/g
    How do I relate these altogether to prove the Galileo thing? Please.
     
  2. jcsd
  3. Jan 28, 2013 #2
    You have found the duration of the flight. Now find the horizontal distance covered in the flight; this is the range in the question. The range will depend on the initial velocity and the angle of projection, so manipulate its formula to show what is required.
     
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