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I have below information like gravity, thrust, my initial x, y and initial velocities. How do I calculate
1. Time to reach the top of the projectile 2. Horizontal displacement during that time

"grav": 0.7,
  "thrust": 10.5,
  "me": {
    "x": 0,
    "y": 180,
    "vx": 4,
    "vy": 0
  }

So far I have tried this formula to calculate vertical displacement (reference here)

enter image description here

For Horizontal displacement, I used t*vx0;

Manali
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    Post what have you tried to solve this? – Ankush soni Oct 03 '15 at 05:13
  • @Manali what coordinate system configuration you have? where are the units,... thrust is applied where and how (if this is really a projectile why thrust?), ... what mass? (or thrust is in m/s^2? ) you can do this by iteratively computing position via D'Lambert Equations like here [fireworks on 3D LED Cube see **Now the particles**](http://stackoverflow.com/a/27214318/2521214) and scan for `vy==0.0` or use [integration of canon ball](http://stackoverflow.com/a/26174961/2521214) – Spektre Oct 03 '15 at 08:27
  • @Spektre consider this to be a 2D problem. I don't have units. I'm assuming thrust is applied at starting point like x0,y0. Mass is negligible. I'm looking at the integration of canon ball answer by you. I updated question with what I tried. Please let me know if I'm missing anything. – Manali Oct 03 '15 at 20:54
  • @Ankushsoni Please check updated question – Manali Oct 03 '15 at 20:55
  • @Manali In which program language you want to implement your formula? – Ankush soni Oct 04 '15 at 05:10
  • @Manali well you still need to specify coordinate system info you provided and usual cases implies: 2D , `-x/+x` (left/right), `-y/+y` (down/up), gravity is in `-y` direction, `(vx,vy)` is initial speed, thrust is either force or acceleration. Now the problems: When you do not know the units how can you integrate? the values must be scaled to compatible unit types, the best way is **SI** `[m,s,m/s,m/s^2,N,kg]` if you have other units need to use compatible conversions or transforms to SI. 2. if thrust is in `m/s^2` then it is acceleration and you do not need mass but where it is applied? – Spektre Oct 04 '15 at 08:07
  • @Manali if it is applied during the flight then in which direction? if it is applied before shot to accelerate then can ignore it if the `vx,vy` is resulting speed but in that case why you have it as input? 3. initial speed `vy=0` is zero which implies you are already at the top peak and start falling down unless thrust is applied. If thrust is acceleration and fully in `+y` direction then the shot will escape gravity ... As you can see there are many things that can be changed here so specify which case you have otherwise is this unanswerable – Spektre Oct 04 '15 at 08:10
  • @Manali when hrust is just for shot acceleration at start then for how long is applied? and the last thing (99.99% true) I hope gravity is constant in the area of interest and bullet/shot has constant properties (solid object)... air friction/drag is ignored ... – Spektre Oct 04 '15 at 08:17

1 Answers1

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If initial vertixal velocity(vy) is zero, assuming gravity is on the y direction, then how is the object ever going to go up to reach the top?

Generally thrown objects reach the top when vy = 0 when t= vy/grav, and x position = t * vx.

MujjinGun
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  • you are missing the thrust input value ... without more info is this unanswerable see the comments ... – Spektre Oct 04 '15 at 08:14