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Find parabola velocity needed to reach a point with air resistance

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Hi, I'm having a very difficult time figuring out how to find the velocity needed to reach a point for a projectile (shot from a cannon) to reach a point with air resistance.

 

time step is constant: 0.02

air resistance is constant: 1 / (1 + 0.02 * drag), where drag is a constant: 2

gravity is constant: -9.81

initial velocity is: 7, 20

mass is constant: 1

 

integration is like so:

 

velocity += gravity * 0.02
velocity *= airResistance

position += velocity * 0.02

 

I'm not much of a math guy, any help would be greatly appreciated :)

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If you express the position after t steps in terms of the initial velocity, you'll get only polynomial expressions. So if you give me t and the position, solving your problem can be reduced to finding a root of a polynomial. You can probable solve this using Newton's method. I can't produce code for you right now, but I might be able to do it tonight.

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Ok thanks. I have no idea what a polynomial is, but I'm going to do some reading.

 

so let's say

 

t = 3,

start position = 0,0,

end position = 10,5

gravity: -9.81

drag: 0.5

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