How do you define angle/velocity for a projectile, if you know final height and distance to reach

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I have a weapons that have a min/max angle, and min/max velocity.

My target height is known, and the distance also.

I know how to compute my maximum distance to see if I can reach, but is there a way base on a range of possible velocity/angle to determine the best value by minimizing time?

Thank

Answer 1

Answer by zigtrig-troy · May 17 at 08:04 PM

@Morphus74 I will answer the question asked in the title. I don't really understand what you wrote after that.

Suppose the projectile is a point mass and there is no air resistance. Suppose you know the total distance the projectile will travel before hitting the ground (assuming the ground is flat), and call that R (for range). Suppose you know the maximum height the projectile ever gets above the ground, and call that H. Then, if the angle between the ground and the initial direction of motion is theta, then theta = arctan(4 H/R). And if the initial speed of the projectile is v, then v = sqrt( g R / s) where s = sin( 2 theta ).

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Morphus74 · May 17 at 08:07 PM 0

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Thank for answer...

Issue is that I don't know the final height... only criteria I have is - Total Distance - Angle between x and y degree - Velocity between x and y unit/second

So the question is how to you find an Angle/Velocity in the range allowed that allow to reach the final distance.

For example What is the best Angle/Velocity if 1. Target is at 200 unit 2. Angle must be between 20-60 Degrees 3. Velocity is between 10-50 unit per second

zigtrig-troy · May 17 at 08:16 PM 0

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The range R, the initial speed v, and the initial angle theta are related by the equation R = (v^2) (sin(2 theta)) / g, where g is the acceleration due to gravity (9.8 m/s^2). Therefore if you know R and theta, you can calculate v. Or if you know R and v, you can calculate theta. (Just do some algebra/trigonometry to rearrange that R = ... equation.)

How do you define angle/velocity for a projectile, if you know final height and distance to reach

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