# The time it takes this thing to travel across 3 points

1. Mar 10, 2012

### Mewtwo

Hey! I have a problem that I have no clue how to solve. So I was hoping you guys could help me. I'm not from an English speaking country so I apologize.

1. The problem statement, all variables and given/known data
A thing is made to travel in water and on land. In water it travels with 20 m/s speed but on land with 25m/s speed. The thing starts at point P on the edge of a pond with radius 50m.

(I drew this picture in paint and what I forgot to include is that the curved line from P to A and the straight line from A to Q are a little bit darker then the other lines, so it seems to me that the thing travels on land from P to A but in water from A to Q).

(a) Show that the time it takes the thing to travel from P to A to Q is:
T(theta)=pi-20+5sin(theta/2)

(b) Give a description of the route that takes the shortest time for the thing to travel.

I think you mean $T(\theta)=\pi - 2\theta + 5\sin{\frac \theta 2}$. But nobody here is going to work it for you. Show us what you have for part (a.)