Q:

the height h (in inches) above the water of a pelican before a dive is modeled by h=-16t^2+70t+50, where t is time (in seconds)a) When does the pelican enter the waterb)How high above the water is the pelican at time t=0 seconds

Accepted Solution

A:
ANSWERa) 5 seconds.b) 50 inches.EXPLANATIONThe height of the pelican is modeled by,[tex]h(t) = - 16t^{2} + 70t + 50[/tex]The pelican enters the when [tex]h(t) = 0[/tex][tex]- 16t^{2} + 70t + 50 = 0[/tex]Divide through by negative 2,[tex]8 {t}^{2} - 35t - 25 = 0[/tex]Factor to obtain[tex](t - 5)(8t + 5) = 0[/tex]This implies that,[tex]t = 5 \: or \: t = - \frac{5}{8} [/tex]Time cannot be negative, therefore the water after 5 seconds.B) The height of the pelican is modeled by [tex]h(t) = - 16t^{2} + 70t + 50[/tex]When [tex]t = 0[/tex][tex]h(0) = - 16(0)^{2} + 70(0) + 50[/tex][tex]h(0) = 50[/tex]The pelican was 50 inches above the water at time t=0.