Question
A person swims in a river aiming to reach exactly opposite point on the bank of a river. His speed of swimming is $$0.5\,m/s$$ at an angle $${120^ \circ }$$ with the direction of flow of water. The speed of water in stream is
A.
$$1.0\,m/s$$
B.
$$0.5\,m/s$$
C.
$$0.25\,m/s$$
D.
$$0.43\,m/s$$
Answer :
$$0.25\,m/s$$
Solution :
Let $$u$$ be the speed of stream and $$v$$ be the speed of person started from $$A.$$ He wants to reach at point $$B$$ directed opposite to $$A.$$
As given, $$v$$ makes an angle of $${120^ \circ }$$ with direction of flow $$u,$$ the resultant of $$v$$ and $$u$$ is along $$AB.$$ From figure
$$\eqalign{ & u = v\sin \theta = v\sin {30^ \circ } \cr & \therefore u = \frac{v}{2} = \frac{{0.5}}{2}\,\,\left( {\because v = 0.5\,m/s} \right) \cr & = 0.25\,m/s \cr} $$
Let $$u$$ be the speed of stream and $$v$$ be the speed of person started from $$A.$$ He wants to reach at point $$B$$ directed opposite to $$A.$$
As given, $$v$$ makes an angle of $${120^ \circ }$$ with direction of flow $$u,$$ the resultant of $$v$$ and $$u$$ is along $$AB.$$ From figure
$$\eqalign{ & u = v\sin \theta = v\sin {30^ \circ } \cr & \therefore u = \frac{v}{2} = \frac{{0.5}}{2}\,\,\left( {\because v = 0.5\,m/s} \right) \cr & = 0.25\,m/s \cr} $$
