CODEWITHSUNDEEP
mathphysics
ricozinn
ricozinn

Reputation: 131

How to find trajectory path if the distance traveled, starting elevation, ending elevation and time in the air are known

I'm trying to find the trajectory an object would take (assuming air drag is negligible and trajectory angle is always between 0 and 90), including peak height. Here's what I know:

For me the problem could be reduced to 2d space, so if an object travels a horizontal distance of 8 meters starting at an elevation of 0 and ending at a relative elevation of -5 meters, and travels for 2 seconds. What was the peak height, and at what point in time did it reach that peak hight.

Also, trying to write this equation in to php, C, or objective C. Thanks

Upvotes: 1

Views: 1508

Answers (1)

Spektre
Spektre

Reputation: 51933

I assume cannon ball like trajectory

  • object has some start velocity
  • not slowing by air (specified by question)
  • only gravity force apply

So

  1. solve the equations to find missing data

    cannon ball

    g=9.81; // [m/s^2]
t=!; // [s] time in air
p0(x0,y0)=!; // [m] start point
p1(x1,y1)=!; // [m] end point
v0(vx0,vy0)=?; // [m/s] start velocity vector

// Y axis free fall with initial velocity
y1=y0+vy0*t-0.5*g*t*t
vy0=(y1-y0+0.5*g*t*t)/t
vy0=(y1-y0)/t+0.5*g*t

// X axis constant speed
vx0=(x1-x0)/t

  2. trajectory path point

    x=x0+vx0*t;
y=y0+vy0*t-0.5*g*t*t;

    where t = <0.0,time_in_air> so for plotting do some for loop through t

  3. peak point:

    vy(t)=vy0-g*t;
// for peak the y velocity is zero so
0.0=vy0-g*t;
t=vy0/g;

    where t is the time when object reach peak point. If you need coordinates then compute them like in bullet #2

Upvotes: 1

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