9.0 River boat problem

  Motion in One Dimension

In river boat problem we come across the following three terms,

${\overrightarrow v _{R}}:$ Velocity of river
${\overrightarrow v _{BR}}:$ Velocity of boat wrt river or velocity of boat in still water
${\overrightarrow v _B}:$ Velocity of boat

So, we can write, $${\overrightarrow v _{BR}} = {\overrightarrow v _B} - {\overrightarrow v _R}$$$${\overrightarrow v _B} = {\overrightarrow v _{BR}} + {\overrightarrow v _R}$$

Note: Students always get confused between ${\overrightarrow v _{BR}}$ and ${\overrightarrow v _B}$.

${\overrightarrow v _{BR}}:$ is the actual capacity of boat. It is due to the power delivered by its engine. ${\overrightarrow v _{BR}}$ will be in the direction boat want to go.

${\overrightarrow v _B}:$ is the absolute velocity of boat. It means the person standing on ground will observe this velocity.

Different conditions in river boat problem are,

1. Downstream
2. Upstream
3. Crosses river in shortest interval of time
4. Reaches the point just opposite from where he started
5. Shortest path