Roy again needs to travel from $A$ to $C$! This time they are diametrically opposite on a circular lake of diameter $120\text{m}.$

(You can move the point $B$ to help visualise the problem.)

Roy is going to run at $5{\text{ms}}^{-1}$ until he reaches the point $B$ and then row his boat at $3{\text{ms}}^{-1}$ the rest of the way.

What is the longest amount of time it could take Roy?

(You are given that the stationary value for total time gives a maximum.)

Express the length of arc $AB$ and the length of line $BC$ in terms of $\theta .$

Use this to express the total time required in terms of $\theta$ and use differentiation find the choice of $\theta$ which gives the maximum/minimum amount of time.

The graph of time against theta looks like this:

As you can see, the longest time uses a combination of running and rowing, but the quickest time does not!

Give your answer to $3$ significant figures