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Find the Trajectory's Launch Angle

  1. Sep 12, 2012 #1
    1. The problem statement, all variables and given/known data

    A cannon fires at a hilltop target with a muzzle velocity of V = 600 ft/s. The
    horizontal and vertical distances to the target are L = 0.5 miles and h = 0.25 miles.
    Determine the elevation angle at which the cannon should be fired.

    L=2640 ft
    h=1320 ft


    2. Relevant equations

    2θ=arcsin([g*R]/V^2)

    3. The attempt at a solution

    2θ=asin([32.2*2640]/360000)

    2θ=asin(.2361)

    θ=6.8282

    This would be the correct angle if the cannon ball were to hit the ground, but the ball is landing on the hilltop. What equation should be used to include the quarter mile in the air?
     

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  3. Sep 12, 2012 #2

    rl.bhat

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    Use the general formula for the projectile.
    h = xtanθ - 0.5gx2/v2cos2θ and solve for θ.
     
  4. Sep 17, 2012 #3
    Thank you!
     
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