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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+50, where h is the height of the bird t and is the amount of time, in seconds, the bird has 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?

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sqdancefan

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Answer:

  3.61 seconds

Step-by-step explanation:

The bird starts 50 feet in the air, so will come down to a height of 40 feet after 3.61 seconds.

We want to solve h = 40.

  40 = -16t^2 +55t +50

  16t^2 -55t -10 = 0

  t = (55 +√(55^2 -4(16)(-10)))/(2(16)) = (55 + √3665)/32 ≈ 3.61060

The bird will be 40 ft above the ground the first time after about 3.61 seconds.

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