Cut the Rope in math class.

I provided my students with a laptop, which had Geogabra on it, and the following picture:

I then showed, on my iPad, how the rockets travels around the point.  When the rope is cut, the rocket will fly tangent to the curve.

I used this in my calculus class and asked "Determine the exact location the rocket should be when the rope is cut"

Students determined the equation of the circle, found the derivative and made it equal to the slope between any point (x,y) on the circle and the co-ordinates of the mouth of the monster (or goblin).
**WARNING, this is a hard question**

After, I was thinking this could be used in lower classes, by changing to one the questions below:

•  allow students to use the tangent button on geogabra, and ask for the reference angle.
• Determine the amount of time which should pass before cutting the rope.
• There are always two tangent lines on a circle through an exterior point, are there two times you could cut the rope in the picture?

There are more I could think of.

My students enjoyed the activity, and feel free to change and adapt as you see necessary.