The following exercise presents a problem similar to an exercise from the previo

Question

The following exercise presents a problem similar to an exercise from the previous section of this chapter. Use Newton's Method to approximate the solution. You are in a boat a miles from the nearest point on the coast (see figure). You are to go to a point Q, which is b miles down the coast and 1 mile inland. You can row at 4 miles per hour and walk at 5 miles per hour. If a = 2, and b = 5, toward what point on the coast should you row in order to reach Q in the least time? (Round your answer to three decimal places.)

Explanation / Answer

solution

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With a = 2 and b = 5, we get
t = SQRT(x^2+2^2)/3 +SQRT((5-x)^2+1)/5

Differentiate on both sides with respect to x

t' = x/(3*SQRT(x^2+4)) +(x-5)/(5*SQRT(x2-10x + 26))
this is zero when x is 1.416 miles.

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