Find the Trajectory's Launch Angle

AI Thread Summary
To determine the launch angle for a cannon firing at a hilltop target, the initial calculation using the equation 2θ=arcsin([g*R]/V^2) yields an angle of approximately 6.83 degrees, assuming the projectile lands on flat ground. However, since the target is elevated, the standard projectile motion equation needs to be applied to account for the height difference. The equation h = xtanθ - 0.5gx^2/V^2cos^2θ should be used to solve for the correct angle θ, considering the vertical distance to the hilltop. This adjustment is crucial for accurately hitting the target. The discussion emphasizes the need for a more complex approach to include the elevation in the trajectory calculation.
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Homework Statement



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


Homework Equations



2θ=arcsin([g*R]/V^2)

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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Use the general formula for the projectile.
h = xtanθ - 0.5gx2/v2cos2θ and solve for θ.
 
Thank you!
 

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