How To Maximize a Cannon's Horizontal Range
In order to maximize a cannon's horizontal range, the angle of the barrel must be set to 45 degrees above the horizontal (assuming all other things like the size of the projectile and the power of the propellant are equal, level ground, and no air resistance). This optimal angle can be proven using the formula for the range of a projectile:
R = V²sin(2θ)/g
Using this formula, we can determine the value of θ that will maximize the value of sin(2θ), which will maximize the range of the projectile since v and g do not change. The maximum value of sin(2θ) is 1, which occurs at sin(90). Therefore the value of θ must be 45 degrees above the horizontal.
R = V²sin(2θ)/g
Using this formula, we can determine the value of θ that will maximize the value of sin(2θ), which will maximize the range of the projectile since v and g do not change. The maximum value of sin(2θ) is 1, which occurs at sin(90). Therefore the value of θ must be 45 degrees above the horizontal.
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