Consider two points on opposite sides of a straight shoreline: a rescuer starts on…
MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives
Problem
Consider two points on opposite sides of a straight shoreline: a rescuer starts on land and a casualty is floating offshore. The rescuer’s land speed is vland and swim speed is vwater, with vland>vwater>0. The rescuer may choose any entry point on the shoreline.
(a) Without performing explicit calculations, explain qualitatively how the optimal entry point shifts as vland increases while vwater remains fixed.
(b) Describe what the optimal entry point would be if vland=vwater and justify your answer using calculus concepts (reference critical points and the shape of the time function).