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Tju [1.3M]
3 years ago
5

In a video game, a bird is flung on a sling shot and follows a parabolic path. The path of the bird can be modeled by the equati

on h=-16t²+55t+4, where h is the height of the bird and t is the amount of time, in seconds, the bird had been in the air. How long will it take the bird to reach a height of 40 feet in the air for the first time?
Mathematics
1 answer:
Novay_Z [31]3 years ago
3 0

Answer:

The bird will take 0.88 seconds to reach a height of 40 feet in the air for the first time

Step-by-step explanation:

we have

h=-16t^2+55t+4

This is a vertical parabola open downward

The vertex represent a maximum

where

h is the height of the bird

t is the amount of time, in seconds, the bird had been in the air

For h=40 ft

substitute in the quadratic equation

40=-16t^2+55t+4

-16t^2+55t+4-40=0

-16t^2+55t-36=0

The formula to solve a quadratic equation of the form

ax^{2} +bx+c=0

is equal to

x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}

in this problem we have

-16t^2+55t-36=0

so

a=-16\\b=55\\c=-36

substitute in the formula

x=\frac{-55\pm\sqrt{55^{2}-4(-16)(-36)}} {2(-16)}

x=\frac{-55\pm\sqrt{721}} {-32}

x=\frac{-55+\sqrt{721}} {-32}=0.88\ sec

x=\frac{-55-\sqrt{721}} {-32}=2.56\ sec

therefore

The bird will take 0.88 seconds to reach a height of 40 feet in the air for the first time

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