Two drones lift off simultaneously from the same point on level ground

MATHEMATICS · Single correct · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

Two drones lift off simultaneously from the same point on level ground. Drone A moves horizontally eastward with velocity

v_A(t)=10t

m/s, where

t

is the time in seconds, while Drone B moves horizontally northward with velocity

v_B(t)=5t^{2}

m/s. Assuming both drones start from rest at the origin, how fast is the straight-line distance between the drones increasing when

t=2\text{ s}

? (a)

24.0\text{ m/s}

(b)

27.7\text{ m/s}

(c)

28.3\text{ m/s}

(d)

22.2\text{ m/s}