A man in a boat is $3$ km from the nearest point of a straight beach. A man is to get to a point \

Question

A man in a boat is $3$ km from the nearest point of a straight beach. A man is to get to a point $6$ km along the beach. The man can row at $4$ km/hr and walk at $5$ km/hr. Show that the time, $T$ hours, taken to get to his destination is given by $T = \frac{\sqrt{x^2+9}}{4} + \frac{6-x}{5}, 0 \le x \le 6$. Where should the man row to along the beach if he is to reach his destination in the least possible time? What is the least time $T$?

Accepted Answer

(a) $T=\frac{\sqrt{x^2+9}}{4}+\frac{6-x}{5}$, $0\le x\le 6$ (shown) (b) Row to a point $4\text{ km}$ from the nearest point on the beach; $T_{\min}=\frac{33}{20}\text{ h}=1.65\text{ h}$

Differentiation - Applications of Differentiation — General

Differentiation - Applications of Differentiation — General

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