Question

A speed of boat is 18 km/h in still
water. It crosses a river of width 2 km
along the shortest path in 7 minutes.
The velocity of the river is​

Answer 1

The speed of the river is 5.5 km/hr.

A speed of boat is 18 km/h in still water. It crosses a river of width 2 km along the shortest path in 7 minutes.

We have to find the velocity of the river.

$\text{velocity of boat}=v_b\\\\\text{velocity of river}=v_r\\\\\text{velocity of boat with respect to river}=v_{br}$

Let the boat makes an angle θ with the speed of boat with the shortest path as shown in figure.

Here component of velocity of boat along vertical direction = shortest distance/time taken

$\implies V_{b}cos\theta=\frac{d}{t}$

$\implies18cos\theta=\frac{2}{\frac{7}{60}}=\frac{120}{7}$

$\implies\theta=cos^{-1}\left(\frac{60}{63}\right)$

Now the component of velocity of boat along horizontal direction = speed of river

$\implies v_bsin\theta=v_r\\\\\implies18\times\frac{\sqrt{63^2-60^2}}{63}\approx5.5=v_r$

Therefore the speed of the river is 5.5 km/hr (approximately).

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Answer 2

Answer:

Explanation:

used basic formula of river boat concept.. See the uploaded answers carefully