A weather balloon is released from ground point P and rises vertically at a constant rate of 4 m/s. Simultaneously, a robotic rover that is initially 30 m east of P begins to drive due west toward P along a straight level path at 1.2 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 dtdD as a function of t. Include correct units.
(c) Determine the exact time t>0 at which dtdD=0. Interpret this result in the context of the scenario.