Aboat heads due east at 3.8 m/s across a river that is 41 m wide. the current is flowing due south at 2.2 m/s. a. what is the resultant velocity of the boat? b. how much time will it take to cross the river? c. how far downstream will it land?
a.4.4 m/s southeast. b. 9.3 seconds. c. 20.46 m.

a. 4.4 m/s southeast

The velocity of the boat has two components:

- A component towards east direction, of magnitude

- A component towards the south direction, of magnitude

Since the two components are perpendicular to  each other, the magnitude of the resultant can be found by using Pythagorean theorem:

and the direction is between the directions of the two components, so southeast.

b. 10.8 s

In this part of the problem, we can just use the velocity of the boat along the direction perpendicular to the river, which is

the distance between the two sides of the river is

d = 41 m

Therefore, the time taken to cross the river is

c. 23.76 m

In order to find how far the boat will land downstream, we have to consider its motion along the direction of the stream, which occurs with a velocity of

We have calculated previously that the time taken to cross the river is

So, the boat will land downstream by a distance of

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1.            c. is smaller

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