A lifeguard is 100 m from point A on a straight shoreline
MATHEMATICS · Multi-part · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
A lifeguard is 100 m from point A on a straight shoreline. A swimmer is at point B in the water, 80 m down-shore from A and 60 m offshore. The lifeguard can run at 7.0 m/s on sand and swim at 1.6 m/s in water. The lifeguard plans to run from his current position to a point C on the shoreline between A and B, then swim straight to B.
(1) Let x be the distance (in meters) from point A to point C along the shoreline. Derive an expression for the total rescue time T(x) in seconds.
(2) Determine the value of x, to the nearest meter, that minimizes T(x).