# A river is flowing with a speed of 1km/hr. A swimmer wants to go to point 'C'. Starting from 'A', he swims with a speed of 5 km/hr at an angle $\theta$ w.r.t the river. If $AB=BC=400 m$. Then

a) time taken by the man is 6 min

b) time taken by the man in 8 min

c) the value of $\theta=45^{\circ}$

d) the value of $\theta=30^{\circ}$

Since $\hat v= 5 km/hr$
$AB= 5 \sin \theta;BC=5 \cos \theta +1$
$5 \sin \theta-5 \cos \theta=1$
$\sin \theta-\cos \theta=\large\frac{1}{5}$
$=>\sin \theta=\large\frac{4}{5}$
$time =\large\frac{AB}{5 \sin \theta}$
$\qquad=\large\frac{0.400}{5 \times {\Large\frac{4}{5}}}=\large\frac{1}{10}$$hr$
$\qquad=6\; mins$
Hence a is the correct answer.
edited May 23, 2014