This question is complicated. But, based on the words, I would say that doubles is the key word. First we have to figure out how far it is between 11 and 2. Now we are going to turn 2 into a 2 digit number, since it is after 12 then we are going to add 12 to this number. 12+2=14. So now we are going to subtract 11 from 14. Leaving us with 3.
Now we know that there are 3 meters at 2, and it doubles every hour.
So we are going to take the square root of 3. 
So that means that it was at 1.732050808 at 1 pm.
Now we are going to take the square root of that number.
Which means that at noon it was at 1.316074013.
And finally take the square root of that number. 
So now we know that at 11 am it was at 1.14720269 meters.
I hope that helps, if you need any further help on this or any other problems just ask.