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Social ScienceYou 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.
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swim 60 m I run 60-X 60 m P X
Expert Answer
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
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R swim 60 m run S 60 X P >I X 60 m
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:
RS2 = QS2 + QR2
Or, RS2 = x2 + 602 = x2 + 3,600
Hence, RS = (x2 + 3,600)1/2
Total travel time T = Time taken while running + time taken while swimming = Distance to ru...
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PS RS Т%3D+ и (60 — х) a +3,600) и x3,600) . Т(х) - (60— х) 2
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Calculus
Functions
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