When a driver jumps from a ledge. the vertical component of his motion can be modeled by the vertical motion model. Suppose the ledge is [i][b]48[/b][/i] feet above the ocean and the initial upward velocity is [b][i]8[/i][/b] feet per second, how long will it take the diver enters the water?

Use a vertical motion model.[br][br]Let [math]v=8[/math] and [math]s=48[/math].[br][br][math]h=-16t^2+vt+s[/math]     [color=#0000ff]Vertical motion model[/color][br][br] [math]=-16t^2+8t+48[/math]     [color=#0000ff]Substitute values.[/color][color=#0000ff][br][/color][br]To find the time when the diver enters the water, let [math]h=0[/math] and solve the resulting equation for [i]t[/i].[br][br][math]0=-16t^2+8t+48[/math]     [color=#0000ff]Write quadratic model.[/color][color=#0000ff][br][/color][br][math]0=\left(-8\right)\left(2t^2-t-6\right)[/math]     [color=#0000ff]Factor out -8.[/color][color=#0000ff][br][/color][br][math]0=\left(-8\right)\left(t-2\right)\left(2t+3\right)[/math]    [color=#0000ff]Factor.[/color][br][br]The solutions are [math]2[/math] and [math]-\frac{3}{2}[/math]. Negative values for time do not make sense, so the only reasonable solution is [math]t=2[/math]. It will take the diver [b][i][color=#ff0000]2 seconds[/color][/i][/b].