Question
The stream of a river is flowing with a speed of $$2\,km/h.$$ A swimmer can swim at a speed of $$4\,km/h.$$ What should be the direction of the swimmer with respect to the flow of the river to cross the river straight?
A.
$${90^ \circ }$$
B.
$${150^ \circ }$$
C.
$${120^ \circ }$$
D.
$${60^ \circ }$$
Answer :
$${120^ \circ }$$
Solution :
To cross the river straight
$$\eqalign{ & {V_s}\sin \theta = {V_r} \cr & \therefore \sin \theta = \frac{{{v_r}}}{{{v_s}}} = \frac{2}{4} = \frac{1}{2} \cr & \therefore \theta = {30^ \circ } \cr} $$
Direction of swimmer with respect to flow
$$ = {90^ \circ } + {30^ \circ } = {120^ \circ }$$
To cross the river straight
$$\eqalign{ & {V_s}\sin \theta = {V_r} \cr & \therefore \sin \theta = \frac{{{v_r}}}{{{v_s}}} = \frac{2}{4} = \frac{1}{2} \cr & \therefore \theta = {30^ \circ } \cr} $$
Direction of swimmer with respect to flow
$$ = {90^ \circ } + {30^ \circ } = {120^ \circ }$$
