How to throw away weapons in the built-in inventory?

What do you mean by "throw away"? The demo scene includes the Drop ability, which is used to drop items from the character's inventory, which I assume is what you want.
 
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The default AssaultRiflePickup prefab (you can find the drop prefab under the Item component, as shown above) has the TrajectoryObject component, so you could create simple script which would call TrajectoryObject.AddForce to add a small force to the object on Start:

C++:
void Start() {
    GetComponent<TrajectoryObject>().AddForce(transform.forward * 0.25f);
}

You'd probably also want to add a Rigidbody to the drop prefab.
 
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