Q. 110 - Precalculus Enhanced with Graphing Utilities

Question

Distance of a Moving Object from a Fixed Point A hot-air balloon, headed due east at an average speed of 15 miles per hour at a constant altitude of 100 feet, passes over an

intersection (see the figure). Find an expression for its distance d (measured in feet) from the intersection t seconds later.

Step-by-Step Solution

Answer

The expression for distance is $d=\sqrt{10000+484t}$

Step 1. Given Information

A hot-air balloon, headed due east at an average speed of 15 miles per hour at a constant altitude of 100 feet,

Step 2. Finding expression for distance

The distance is the hypotenuse of a right triangle. 

Height$=100ft$

Path of the balloon has speed $$\begin{gathered} =15miles=15\times 5280\raisebox{1ex}{$ft$}\!\left/ \!\raisebox{-1ex}{$hr$}\right. \\ =22 \raisebox{1ex}{$ft$}\!\left/ \!\raisebox{-1ex}{$sec$}\right. \end{gathered}$$

$$\begin{gathered} d^2={100}^2+22t^2 \\ {d}^2=10000+484t \\ d=\sqrt{10000+484t} \end{gathered}$$