I have two objects in a three dimensional world. One is a ballistic projectile: that is, it is free-falling with some known gravitational acceleration. The other is a catcher that travels with constant velocity and is not subject to gravity. I want to calculate the vector that the catcher must travel along in order to intercept and catch the falling projectile (or the position of intercept between the catcher and the projectile).
By my reckoning, the problem can be formulated into equations like this:
Intercept position = Catcher start position + Catcher velocity * Intercept time
Intercept position = Projectile start position + Projectile start velocity * time + 1/2 * Gravitational acceleration * Intercept time^2
...where all the named variables except intercept time are three-dimensional vectors. Within those equations, I know:
- The catcher and projectile start positions
- The projectile's current velocity
- The projectile's gravitational acceleration
- The magnitude of the catcher's velocity.
I don't know, and could solve the problem by finding out any one of:
- The direction of the catcher's velocity
- The intercept position
- the intercept time
...but I have really struggled to make any headway finding a solution to these equations. Can anyone help me out? Is there something missing from/incorrect about my approach here?