Question

1. a hot air balloon is dropping from a height above the ground at a steady rate of 8 feet per second. it starts from a height of 765 feet. after t seconds it has hit a height of 421 feet. set up and solve an equation for the value of t.

Explanation:

Step1: Define the height formula

The balloon starts at height \( h_0 = 765 \) feet and descends at a rate of \( r = 8 \) feet per second. The height \( h \) after \( t \) seconds is given by \( h = h_0 - rt \). We know \( h = 421 \), so the equation is \( 421 = 765 - 8t \).

Step2: Solve for t

First, subtract 765 from both sides: \( 421 - 765 = -8t \). Calculate \( 421 - 765 = -344 \), so \( -344 = -8t \). Then divide both sides by -8: \( t = \frac{-344}{-8} = 43 \).

Answer:

\( t = 43 \)