A streetlamp stands at a point on a straight sidewalk
MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation
Problem
A 5 m streetlamp stands at a point on a straight sidewalk. A 1.7 m tall jogger moves away from the lamp at 1.2 m/s, while at the same instant a 2.2 m tall delivery robot approaches the lamp from the opposite direction at 0.8 m/s. The jogger is 4 m from the lamp and the robot is 3 m from the lamp at that instant. Each casts a shadow on the ground away from the lamp. At that moment, at what rate (in meters per second) is the distance between the two shadow tips changing (positive if increasing)?
(a) −0.39
(b) 1.43
(c) 0.39
(d) 3.25