An engineering student is in an "egg dropping contest." The goal is to create a container for an egg so it can be dropped from a height of [b][i]32[/i][/b] feet without breaking the egg. To the nearest tenth of a second, about how long will it take for the egg's container to hit the ground? Assume there is no air resistance.

Write an equation to model the egg container's height [i][b]h[/b][/i] as function of time [b][i]t[/i][/b], where the initial height [math]s=32[/math].[br][br][math]h=-16t^2+[/math] [color=#ff0000][i]s[/i][/color]     [color=#0000ff]Write falling object model.[br][br][/color][math]h=-16t^2+[/math] [color=#ff0000]32[/color]     [color=#0000ff]Substitute 32 for [i]s[/i].[br][br][/color]The falling object model for the egg container is [math]h=-16t^2+32[/math]

[b]MAKE A TABLE[/b] One way to solve the problem is to find the height [i][b]h[/b][/i] for different values of time [i][b]t[/b][/i] in the function [math]h=-16t^2+32[/math]. Organize the data in a table. The egg container will hit the ground when [math]h=0[/math].

From the table, you can see that [math]h=0[/math] between [b][i]1.4[/i][/b] and [b][i]1.5[/i][/b] seconds. The egg container will take between [b][i]1.4[/i][/b] and [b][i]1.5[/i][/b] seconds to hit the ground.[br]

[b]USE AN EQUATION.[/b] Another way to approach the problem is to solve the quadratic equation for the time [b][i]t[/i][/b] that gives a height of [math]h=0[/math] feet.[br][br][color=#0000ff][i]h[/i][/color] = [math]-16t^2+32[/math]       [color=#0000ff]Write falling egg model.[/color][br][br][color=#0000ff]0[/color] = [math]-16t^2+32[/math]       [color=#0000ff]Substitute 0 for [i]h[/i].[/color][br][br][math]-32=-16t^2[/math]        [color=#0000ff]Subtract 32 from each side.[/color][br][br][math]2=t^2[/math]         [color=#0000ff]Divide each side by -16.[/color][br][br][math]\sqrt{2}=t^2[/math]         [color=#0000ff]Find positive square root.[br][/color][br][math]1.4\approx t[/math]         [color=#0000ff]Use a calculator.[/color][br]The egg container will hit the ground in about 1.4 seconds. You can ignore the negative square root, because -1.4 seconds is not a reasonable solution.