Chapter 9.1, Problem 18P

A relief organization flew over a village and dropped a package of food and medicine. The plane is flying at 1000 feet. The function $h=-16t^2+1000$ gives the package’s height $h$ above the ground (in feet) after $t$ second. Graph the function. How many seconds does it take for the package to hit the ground?

To determine

To find the time taken for the package to hit the ground by sketching a graph.

Answer to Problem 18P

The time taken by the package to hit the ground is $t\approx 7.91\sec$ .

Explanation of Solution

Given information:

The plane is flying at $1000ft$ high and the given function is $h=-16t^2+1000$ .

Graph:

  

Interpretation:

$t$	$h$
$0$	$1000$
$2$	$936$
$4$	$744$
$6$	$424$

Using the above table, the graph has been plotted.

Consider the given function $h=-16t^2+1000$ .

The package hits the ground when $h=0$ ,

  $\begin{array}{l}-16t^2+1000=0\\ 16t^2=1000\\ t^2=62.5\\ t\approx 7.91\sec \end{array}$

Therefore, the time taken by the package is $t\approx 7.91\sec$ .