Two cyclists depart from perpendicular roads that intersect at point

MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

O

. Cyclist A passed through

O

heading east

10

minutes ago and continues due east at a constant speed of

20\text{ km/h}

. Cyclist B is riding due north toward

O

at a constant speed of

15\text{ km/h}

and will reach

O

exactly

5

minutes from now. (a) Express the distance

D

between the cyclists as a function of time

t

, where

t=0

represents the instant described above. (b) Determine

\dfrac{dD}{dt}

t=0

. State appropriate units and indicate whether the distance is increasing or decreasing at that instant. (c) Find the time (relative to

t=0

) at which the cyclists are closest together. Justify your answer analytically. (d) Calculate that minimum distance.