Boat and Arc Length problem

Question

Boat men wants to reach at exact opposite point of river,which is 40m wide. Speed of boat in still water is 5m/sec and that of river is 2 m/sec . Find following 1- Angle at which he needs to start journey from starting point. 2-length of arc (shortest possible) , which boat would travel.enter image description here

Answer 1

Hint 1

To reach the exact opposite point, component of velocity along the river should be zero.

Hence, the angle with the river bank is such that $5 \cos{\theta} = 2$.

$$\theta = \arccos{\frac{2}{5}} \approx 66.4 \deg$$

Hint 2

Length of shortest arc length will be $40 m$ since path of boat is a straight line.

Related Problem for you to try

Solve the problem if speed of boat is $2 \frac{m}{s}$ and speed of water is $5 \frac{m}{s}$. That is, the speeds are interchanged.