Question

a hot - air balloon, headed due east at an average speed of 15 miles per hour at a constant altitude of 175 feet, passes over an intersection (see the figure). find an expression for its distance d (measured in feet) from the intersection t seconds later.

Explanation:

Step1: Convert speed to feet - per - second

First, convert 15 miles per hour to feet per second. Since 1 mile = 5280 feet and 1 hour = 3600 seconds, the speed $v$ in feet per second is $v = 15\times\frac{5280}{3600}=22$ feet per second.

Step2: Use the Pythagorean theorem

The balloon is at a constant altitude of 175 feet. The horizontal distance $x$ it travels in $t$ seconds is $x = 22t$ feet. Let the distance from the intersection be $d$. By the Pythagorean theorem $d=\sqrt{(22t)^{2}+175^{2}}=\sqrt{484t^{2} + 30625}$.

Answer:

$d=\sqrt{484t^{2}+30625}$