At time seconds Drone P is located at the origin in a horizontal coordinate plane and…
MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
At time t=0 seconds Drone P is located at the origin (0,0) in a horizontal coordinate plane and flies due east at a constant speed of 12 m/s. At the same instant Drone Q is located at the point (0,200) (200 m north of the origin) and flies due south at a constant speed of 8 m/s. The positions of the drones remain confined to the xy-plane.
(a) Write an expression for the distance s(t) between the two drones as a function of t.
(b) Derive a formula for dtds in terms of t.
(c) Determine the time t (to the nearest hundredth of a second) at which the drones are closest to each other. Provide evidence that this time corresponds to a minimum distance.
(d) Calculate that minimum distance, including appropriate units.