Minimum linear velocity and maximum angular velocity in a pursuit problem: Use of calculus

Abstract

A ship/boat is travelling parallel to a river bank and a patrol vehicle is approaching the river along a road perpendicular to the river bank, i.e., the ship and the vehicle are moving at right angles to each other with uniform speeds. The patrol vehicle focuses a search light on the ship at all time instants, implying continuous rotation of the search light beam. In this article the relative velocity and acceleration between the ship and the vehicle as well as the angular velocity and acceleration of the beam are determined. Some numerical examples are also cited.