21st October 2019

calculus7
11

What angle maximizes the range of a projectile?

To maximize the range with respect to the firing angle θ we differentiate R with respect to θ and set this equal to 0. g 2 ∙ cos ( ) ∙ 0 therefore π 2 from which we obtain θ π 4 or 45 degrees. Suppose now we fire the projectile up a ramp which makes an angle α with respect to the horizontal. 1.

Likewise, people ask, what is the angle for maximum range?

Maximum Range. Imagine a cannonball launched from a cannon at three different launch angles - 30-degrees, 45-degrees, and 60-degrees. The launch speed is held constant; only the angle is changed. Imagine as well that the cannonballs do not encounter a significant amount of air resistance.

How does the angle affect the distance?

Vertical Distance. The vertical distance, or height, of the ball when thrown or kicked increases when you launch it at a greater angle. As the ball travels upward on its parabolic flight path, the vertical distance it travels decreases because the vertical velocity is decreasing against the push of gravity.

What is the best angle to throw a ball?

Most people know that a ball without air resistance (traditional projectile motion) goes the farthest if you throw it at a 45 degree angle.
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