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 $\theta=30^{\circ}$

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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 $\theta=30^{\circ}$

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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.

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