High speed, long distance projectiles and tracking via radio
 

I have quite an interesting topic at hand to discuss here so I'll get right to it.

I have acquired a custom machined brass and aluminium projectile from a friend in Canada that will be launched from a homemade device at close to supersonic speeds. The projectile has an estimated range of about 4km due to its low drag coefficient and high density.

The problem is finding the projectile after the launch. I have discussed this matter over several hundred posts with some very intelligent people on a forum but we can't decide on what method is best to track the projectile.

The projectile is hollow with a cavity 14mm in diameter and about 60mm long. Is it possible to build an FM transmitter to fit inside this projectile and transmit distances around 100m? The projectile may be buried in sand upon impact so it will need to transmit out of the hole it is in. Due to projectile drag, the antenna cannot extend more than about 2 inches outside the projectile.

I'm led to believe i'd need a transmitter in the GHz region to have such a small antenna. I assume coiling the antenna around the base of the projectile will limit range?

To break down my questions:

1. Can some form of radio transmitter be built on a circuit to fit inside a 14mm x 60mm cavity?
2. Can such a transmitter have a range of around 100m with a short antenna?

I'm aware I probably should have done more research on this topic but I figured I would find out if it is even possible first.

P.S. I am a poor university student on a budget of no more than $50 (incl. receiver).

I appreciate any help.

Cheers.