A dog is at the centre of a circular pond 200 m in diameter and a duck is swimming around the outer edge of the pond. The dog starts towards the duck swimming at the same speed as the duck. If the dog continually keeps in line with the centre of the pond and the duck, how far must he swim before reaching the duck? Thanks for help.
This would be much easier to visualize if I could upload a diagram, but unfortunately I can't. So I will try and give a brief description of what actually happens.
Draw a semi circle with a diameter of 200 m, and the label the centre "A". Draw a perpendicular line from from centre "A" to a point on the circumference, which will call "B", which will be the radius =100m. The dog starts swimming from the centre A, within the 1st quadrant, in an arc from A to B. This arc, AB, will form a smaller circle within the 1st quadrant, whose diameter is the radius of semi circle, which is = 100 meters.
The circumference of this smaller circle within the semi circle will be=100π. By the time the dog reaches the duck at point B, he/she has already swum 1/2 of circumference of the smaller circle, or
100π/2 =157.08 meters! And that is how much the dog will have to swimm to meet the duck!.
And that is my take on it. Now, you guys with fancy graphing implements would see it clearly if you drew a picture of it.
