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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 water
b)How high above the water is the pelican at time t=0 seconds

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ANSWER

a) 5 seconds.

b) 50 inches.

EXPLANATION

The 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.

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