A runner starts at the origin and moves due north along the y-axis
MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
A runner starts at the origin and moves due north along the y-axis. Her speed at time t seconds is vR(t)=5+0.2t m/s. At the same instant (t = 0), a cyclist located 60 m west of the origin begins riding due east along the x-axis at a constant 8 m/s.
Assume a coordinate system with origin at the runner’s starting point, x-axis east, and y-axis north.
(a) Find the position of the runner and the position of the cyclist as functions of time for t ≥ 0 s.
(b) At t = 10 s, calculate the rate at which the distance between the runner and the cyclist is changing. Include appropriate units.