To find out how long it will take for the bird to reach a height of 40 feet, we can set h equal to 40 and solve for t:
40 = -16t^2 + 55t + 50
Rearranging the equation, we get:
16t^2 - 55t - 10 = 0
Now, we can solve for t by using the quadratic formula:
t = (-(-55) ± √((-55)^2 - 4(16)(-10))) / 2(16)
t = (55 ± √(55^2 + 640)) / 32
t = (55 ± √(3025 + 640)) / 32
t = (55 ± √(3665)) / 32
t ≈ (55 ± 60.54) / 32
Taking the positive value for t:
t = (55 + 60.54) / 32
t ≈ 3.84 seconds
Therefore, it will take the bird approximately 3.84 seconds to reach a height of 40 feet in the air for the first time.
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=-16t^2+55t+50 where h is the height of the bird and t 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? Round your answer to the nearest hundredth.
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