Physics > Motion in One Dimension > 9.0 River boat problem
Motion in One Dimension
1.0 Introduction
2.0 Kinematic variables
2.1 Distance and displacement
2.2 Average speed and velocity
2.3 Instantaneous speed and velocity
2.4 Average and instantaneous acceleration
3.0 Motion in one dimension
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
4.0 Derivation of the kinematics equation
5.0 Vertical motion under gravity
5.1 Basic terminologies for motion under gravity
5.2 Detailed concept of motion under gravity
5.3 Solved examples
6.0 Analysis of motion through graph
6.1 Displacement - time graph
6.2 Velocity - time graph
6.3 Area under the graph
6.4 Solved examples
7.0 Relative motion
7.1 Relative displacement
7.2 Relative velocity
7.3 Relative acceleration
7.4 Illustration of relative motion
7.5 Application of relative motion
8.0 Simultaneous motion of two bodies
9.0 River boat problem
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
10.0 Aircraft-wind problem
11.0 Rain problem
9.2 Upstream
2.2 Average speed and velocity
2.3 Instantaneous speed and velocity
2.4 Average and instantaneous acceleration
3.2 Motion in a straight line with uniform acceleration
3.3 Motion in a straight line with non-uniform acceleration
5.2 Detailed concept of motion under gravity
5.3 Solved examples
6.2 Velocity - time graph
6.3 Area under the graph
6.4 Solved examples
7.2 Relative velocity
7.3 Relative acceleration
7.4 Illustration of relative motion
7.5 Application of relative motion
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
When the boat goes opposite to the flow of the river, it is considered to be upstream.
Consider a river is flowing from left to right with velocity $v_R$.
So, for upstream, $v_{BR}$ should be in the direction opposite to the river flow.
We can write,
${\overrightarrow v _{BR}} = -{v_{BR}}\widehat i$
${\overrightarrow v _R} = {v_R}\widehat i$
So, the observer standing on shore will observe the velocity of boat $\left( {{v_B}} \right)$ as,
$${\overrightarrow v _{BR}} = {\overrightarrow v _B} - {\overrightarrow v _R}$$$${\overrightarrow v _B} = {\overrightarrow v _{BR}} + {\overrightarrow v _R}$$$${\overrightarrow v _B} = \left( {-{v_{BR}} + {v_R}} \right)\widehat i$$or$${{\vec v}_B} = - \left( {{v_{BR}} - {v_R}} \right)\hat i$$
