Finding the Minimum Distance Between Two Projectiles in Projectile Physics

[aim1732]

The problem is regarding two projectiles whose distance of separation is known.Their initial velocities and angle of projection are known, plus these angles are complementary and velocities are known to be equal.It is also known that the two projectiles do no colllide.
We are required to find the minimum distance b/w the projectiles.

I wrote down the displacement vectors for the two(with origin at one of the points of projection,of course).Then I subtracted them and found out the magnitude of the vector.Since this is the distance b/w them I differentiated this w.r.t time(as it is the only variable here) and put that equal to zero to minimize it.Then I put the t obtained back in the eqn. for minimum distance.
Is this right? Because the book does not think so!

 

[Mentallic]

Could you please provide some more information? Even a picture would be greatly helpful.

For e.g. are these objects being projected in opposite directions or in the same direction? Are we finding the minimum distance between the projectiles once they touch the ground again, or at some point during their flight?

 

[aim1732]

Sorry. They are projected towards each other and are initially 20m apart. The velocities are 17.32 m/s for both and angles 30 and 60. The minimum distance is when they are in flight. Anyways there ranges are same so final distance is unchanged.