A streetlight of height 4.5 m is fixed on level ground
MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
A streetlight of height 4.5 m is fixed on level ground. A pedestrian who is 1.8 m tall walks directly away from the streetlight along a straight sidewalk at a constant speed of 1.2 m/s.
Let x be the pedestrian’s distance from the base of the streetlight (in metres) and s the length of the pedestrian’s shadow (in metres), both measured at time t seconds.
(a) When the pedestrian is exactly 10 m from the streetlight, calculate ds/dt, the instantaneous rate at which the shadow length is changing.
(b) At the same instant, determine the velocity of the tip of the shadow relative to the ground. Express the final answer in metres per second and indicate clearly whether the tip is moving toward or away from the streetlight.
(c) Interpret the sign of ds/dt obtained in part (a) in the context of the scenario.