A river 400 m wide is flowing at a rate of $2 m/s$ . A boat is sailing at a velocity of 10.0 m/s with respect to the water, in a direction perpendicular to the river. Find the time (in seconds) taken by the person to reach the opposite bank at a point directly opposite to its starting point considering that after reaching the opposite bank, the person walks at $4 m/s$ if needed to reach the point directly opposite to its starting point.

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Solution

As it is given that boat is sailing in a direction normal to current.
Crossing velocity of boat is $= 10 m/s$ .
So time taken by the boat to reach the other bank is $= \frac{400}{10} = 40 s$
Drift due to flow of river is = Drift velocity $\times$ time to cross the river.
Drift $= 2 \times 40 = 80 m$
therefore, additional time $= \frac{80}{4} = 20 seconds$
So, the total time is $60 seconds$

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Similar questions

A river 400 m wide is flowing at a rate of 2.0 m/s. A boat is sailing at a velocity of 10 m/s with respect to the water, in a direction perpendicular to the river.

(a) Find the time taken by the boat to reach the opposite bank.

(b)How far from the point directly opposite to the starting point does the boat reach the opposite bank ?

Q. A 400-m wide river is flowing at a rate of

2.0 m s^{- 1}

. A boat is sailing with a velocity of

10 m s^{- 1}

with respect to the water, in a direction perpendicular to the river.
a. Find the time taken by the boat to reach the opposite bank.
b. How far from the point directly opposite to the starting point does the boat reach the opposite bank?
c. In what direction does the boat actually move?

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