Question

Asked Jun 28, 2019

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You must get from a point P on the straight shore of a lake to a stranded swimmer who is 60 meters from a point Q, on the shore that is 60 m from you (see figure). If you can swim at a speed of 2 m/s and run at a speed of 4 m/s, at what point along the shore, x meters from Q, should you stop running and start swimming if you want to reach the swimmer in the minimum time?

a. Given the above write the function T that gives the travel time as a function of x, where 0 <= x <= 60.

Step 1

Let, "u" be the velocity at which you can swim and "v" be the velocity at which you can run.

u = 2 m / s

Please see the diagram on the white board. I have marked two more points "R" and "S". Please look at the triangle QRS.

v = 4 m / s

Step 2

RS = distance that you have to swim through.

Triangle QRS is a right angled triangle. Hence, make use of Pythagoras theorm to write the following equation:

RS^{2} = QS^{2} + QR^{2}

Or, RS^{2} = x^{2} + 60^{2} = x^{2} + 3,600

Hence, RS = (x^{2} + 3,600)^{1/2}

Step 3

Total travel time T = Time taken while running + time taken while swimming = Distance to ru...

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