A weather balloon is released from ground point and rises vertically at a constant rate of

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

Problem

A weather balloon is released from ground point

P

and rises vertically at a constant rate of

4\text{ m/s}

. Simultaneously, a robotic rover that is initially

30\text{ m}

east of

P

begins to drive due west toward

P

along a straight level path at

1.2\text{ m/s}

. Let

t

be the time (in seconds) after both motions start. (a) Express the distance

D(t)

between the balloon and the rover in terms of

t

. Clearly indicate all intermediate quantities you introduce. (b) Compute

\dfrac{dD}{dt}

as a function of

t

. Include correct units. (c) Determine the exact time

t>0

at which

\dfrac{dD}{dt}=0

. Interpret this result in the context of the scenario.