How do I create Sling-Shot like propulsion?

This is my first post, so please excuse any errors in my level of detail or wording. But ultimately, I am trying to accomplish this:

My character (who is on a linear path with a constant velocity, not user controlled) gets tossed into the air and will attach itself to a spinning wheel (think like a giant clock tower gear via a touch and hold control). I’m able to get this far by coding with colliders and parenting the wheel to my character…but what I have trouble with is letting go and having the character “sling-shot” off the wheel naturally, so that you take off in the direction and speed the wheel was rotating where you let go. The best example to reference would be the graspable wheels in Little Big Planet.

I have tried to research this for hours but to no avail. Any help or guidance would be greatly appreciated, thanks!

Thanks @hexagonius. I was able to finally think up and play around with the solution! My code is pasted below, I had to manually multiply the distance and speed to seem more natural. Let me know if anyone thinks this could be simplified or made smoother. Thanks again! **On a side note, the SlingShot() function is called from another script that controls the touch gestures.

public class SlingShotScript : MonoBehaviour {

    private Rigidbody2D body;
    private Vector2 prevLoc;
    private Vector2 currLoc;
    private Vector2 distance;
    private float speed;

    void Awake()
    {
        prevLoc = transform.position;
    }

    void Start()
    {
        body = GetComponent<Rigidbody2D>();
    }

    public void SlingShot()
    {
        distance = (currLoc - prevLoc) * 10f;
        speed = distance.magnitude * 2f;
        body.AddForce(distance * speed, ForceMode2D.Impulse);
    }

    void Update()
    {
        prevLoc = transform.position;
    }

    void LateUpdate()
    {
        currLoc = transform.position;        
    }
}