Question

A river 400m wide is flowing at a rate of 4m/s. A boat sailing at a velocity of 4m/s with respect to the water, in a direction perpendicular to the river. Calculate the time taken to reach the opposite bank and the horizontal distance moved by the boat

Answer 1

Answer:

As the velocity of the boat and the river is same there remains constant direction of the boat which gives the $\bold{width\:of\:the\:river=Distance \:covered\:by\:boat}$

For detailed explanation refer the whole answer. :)

$\huge{Explanation:}$

Given that :-

$Tan\theta=\frac{DE}{AD}=\frac{4}{4}=1$

Width of river = 400m

Velocity of river = 4m/s

Velocity of boat = 4m/s

$\underline{(a) \:Time\: taken \:by\: the\: boat\: to\:reach\:the\:opposite\:bank}$

$\bf{Time=\frac{Distance}{Speed}}$

$Time=\frac{400}{4}$

$\bf{Time=100\:seconds}$

$\underline{(b)\:Horizontal \:distance\:covered\:by\:the\:boat}$

In ∆ABC, $tan\theta=\frac{BC}{AB}=\frac{BC}{400}=1$

$\bf{BC=400m}$

•°• Time taken by the boat to reach opposite bank is 100 seconds!

And, Distance traveled is 400 metres!