Question

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 equation 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?

Answer 1

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

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√(721)} {-32}`

`x=\frac{-55+√(721)} {-32}=0.88\ sec`

`x=\frac{-55-√(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