Jane is 2mi offshore in a boat and wishes to reach a coastal village 6mi down a straight shoreline from the point nearest the boat. She can row 2mph and can walk 5mph. Where should she land her boat to reach the village in the least amount of time?

Question

I'm totally stumped by this question. So far I have the picture of the problem, and that's about it. Help please?!

Thank you

Answer 1

This is a good Calculus question.

label your diagram as follows
A - position of boat
B - point on shore closest to A
C- point on shore where he should row to (our answer)
V - position of the village

Clearly ABC is a right angle,
let BC = x, then CV = 6-x
AB = 2
AC = √(x^2 + 4)

Time in water = √(x^2 + 4)/2
time along shore = (6-x)/5

Time = (1/2)(x^2 + 4)^(1/2) + 6/5 - x/5

dTime/dx = (1/4)(x^2+4)^(-1/2)(2x) - 1/5

set this equal to zero and solve for x

let me know what you got.

Answer 2

4/sqrt(21)? or 0.87287