Aboat moves through the water of a river at 4.72 m/s relative to the water, regardless of the boat’s direction. if the current is flowing at 3.86 m/s, how long does it take the boat to complete a trip consisting of a 297 m displacement downstream followed by a 389 m displacement upstream? answer in units of s.

Total time taken by boat to cover all the displacement = 452.3254 sec

Explanation:

We have given speed of boat = 4.72 m/sec

Speed of current flowing = 3.86 m./sec

In downstream relative speed of boat = speed of boat + speed of current flowing = 4.72+3.86 = 8.58 m/sec

Distance traveled downstream = 297 m

So time taken by boat to travel 297 m downstream

In upstream relative speed of speed = speed of boat - speed of current flowing = 4.72 -3.86 = 0.86 m/sec

Distance traveled in upstream = 389 m

So time taken to travel 289 m upstream

So total time

486.95s

Explanation:

Let the velocity of the boat be and that of the river be .

When the boat is moving downstream, the resultant velocity is given by;

Recall that

Given; downstream displacement, d = 297m. Therefore by equation (1);

where is the time taken to travel downstream displacement.

When the boat is moving upstream it is moving directly against the river current, hence its resultant velocity in this case becomes;

The time taken upstream is then calculated as follows given that the upstream displacement is 389m, according to equation (1);

therefore

Hence the total time taken by the boat to complete its trip as specified is given as follows;

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