9.4 Reaches the point just opposite from where he started

2.1 Distance and displacement
2.2 Average speed and velocity
2.3 Instantaneous speed and velocity
2.4 Average and instantaneous acceleration

3.1 Motion in a straight line with uniform velocity
3.2 Motion in a straight line with uniform acceleration
3.3 Motion in a straight line with non-uniform acceleration

4.1 Graphical method
4.2 Calculus method

5.1 Basic terminologies for motion under gravity
5.2 Detailed concept of motion under gravity
5.3 Solved examples

6.1 Displacement - time graph
6.2 Velocity - time graph
6.3 Area under the graph
6.4 Solved examples

7.1 Relative displacement
7.2 Relative velocity
7.3 Relative acceleration
7.4 Illustration of relative motion
7.5 Application of relative motion

8.1 Solved examples

9.1 Downstream
9.2 Upstream
9.3 Crosses the river in shortest interval of time
9.4 Reaches the point just opposite from where he started
9.5 River-man problem
9.6 Solved examples

11.1 Solved examples

If the boat started from $A$, it should reach $B$.

So, the absolute velocity of the boat should be along $AB$. Therefore, the boat should travel as shown in the figure.

So, $${v_B} = {v_{BR}}\cos \theta $$$${v_R} = {v_{BR}}\sin \theta $$
It is crossing river due to the velocity along $y$ axis.

Here velocity along $y$ axis is $v_B$.

So, time taken to cross the river is, $$t = \frac{d}{{{v_B}}}$$ or $$t = \frac{d}{{{v_{BR}}\cos \theta }}$$

Note: This case is only valid when ${v_{BR}} > {v_R}$.