The time it takes this thing to travel across 3 points

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SUMMARY

The discussion centers on a physics problem involving a traveling object that moves at different speeds in water (20 m/s) and on land (25 m/s). The object starts at point P, travels to point A on land, and then to point Q in water, with the goal of determining the time taken for this journey. The correct formula for the time taken is established as T(θ) = π - 2θ + 5sin(θ/2). Participants emphasize the importance of showing work for part (a) to facilitate assistance.

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Mewtwo
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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.

Homework Statement


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.
358a23l.jpg

(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.

Thanks in advance!
 
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Mewtwo said:
(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)

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.)
 
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