A river has a steady speed of 0.550 m/s. A student swims upstream a distance of 1.00 km and swims back to the starting point. If the student can swim at a speed of 1.50 m/s in still water, how long does the trip take (swimming up and down in the current)?If the water were still, by how much would the trip be longer or shorter?

Explanation:

Here the steady speed of the river water relative to ground is

Speed of the boy relative to still water is

Here we are considering +ve speed along along +ve x-axis and -ve speed along -ve x-axis

Therefore the speed of boy relative to the ground upstream is:

And the speed of boy relative to the ground downstream is:

The distance covered in upstream trip d₁=1.0km=1000m and the distance covered in downstream is d₂=1.0km=1000m

Since time taken by a person is to cover distance d with speed v given by:

The total time taken for one trip is:

no. dot product   =0 when vecs at right angles

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