- #1

- 4

- 0

I was thinking, what If there were two bodies (represented by points) in space (two dimensional space to keep it simple) with known position at time zero, where the first is moving at a known velocity and the second moving at an unknown velocity.

There is, however, a restriction on the velocity of the second body: it can have any direction, however, it must have a specific speed, i.e. magnitude.

Let Vf = velocity of the first body,

Df = position of first body at time zero

Let Vs = direction of the second body's velocity (unit vector),

Ss = speed of the second body (magnitude of velocity),

Ds = position of second body at time zero

If Vf, Df, Ss, and Ds are known, how then can I determine Vs such that the two bodies collide in the shortest time possible?

As well, how can I determine whether or not it is possible for the two bodies to collide? For example, if |Vf| ≥ Ss and Vf points away from Ds than the two bodies would have no chance of colliding no matter what Vs is, providing |Vs| = one.

It seems to me that this may require calculus to solve, especially due to the parameter of the shortest time possible. This is the main reason why I am not sure whether this post should be in this forum or the calculus forum.

Thank you for any help.