a)time taken by the man in 6 mins

b) time taken by the man in 8 mins

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

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

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a)time taken by the man in 6 mins

b) time taken by the man in 8 mins

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

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

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Answer: Time taken to get across is 6 mins.

Since $ AB=BC$

We use vector addition and write $5 \sin \theta=5\ cos \theta+1$

$\Rightarrow 5(\sin \theta-\cos \theta)=1\; \rightarrow $$\sin \theta-\cos \theta=\large\frac{1}{5} \rightarrow $$\theta=53^{\circ}$

$\therefore$ the two options with $\theta = 45$ and $\theta = 30$ are incorrect.

Let;s calculate the time taken to get across as $ t =\large\frac{AB}{5 \sin \theta}$

$\qquad=\large\frac{0.400}{5 \times \Large\frac{4}{5}}$$=\large\frac{1}{10}$$\;hrs$$=\large\frac{1}{10} $$\times 60\; min = 6\; min$

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