Question

A man crosses a river in a boat .If he cross the river in minimum time he takes 10min with a drift of 120m.If he crosses the river taking shortest path,he takes 12.5min,find velocity of the boat with respect to water,width of river and speed of river​

Answer 1

Answer:

Width of river = 200 m

speed of river flow = 12 meter/min

speed of boat = 20 meter/min

Explanation:

As we know that the minimum time to cross the river is given as

$t = \frac{w}{v_b}$

$10 min = \frac{w}{v_b}$

now if the boat drift along the river by 120 meter

So here flow of river water speed is given as

$v_r = \frac{drift}{time}$

$v_r = \frac{120}{10} = 12 meter/min$

now when it comes back to with shortest path then

$v_b sin\theta = v_r$

$v_b sin\theta = 12$

also we have

$\frac{w}{v_b cos\theta} = 12.5 min$

$\frac{10v_b}{v_b cos\theta} = 12.5 min$

$cos\theta = 0.8$

$\theta = 37 degree$

so we have

$v_b sin37 = 12$

$v_b = 20 meter/min$

now we have

$w = 10 v_b$

$w = 200 meter$

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Topic : River crossing problem

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