A swimmer is on a small island located 500 m north of a straight beach
MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation
Problem
A swimmer is on a small island located 500 m north of a straight beach. The swimmer needs to reach a lifeguard station that is 1,000 m east of the point on the beach closest to the island. The swimmer swims at 2 m/s and can run along the beach at 5 m/s. Suppose the swimmer lands at a point that is x meters east of the nearest point on the beach and then runs to the station. For which of the following landing points does the total travel time take its minimum value?
(a) x=0 m
(b) x=500 m
(c) x=300 m
(d) x=102 m