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
y 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.
To find the time it takes for the bird to reach a height of 40 feet, we need to set the equation h = 40 and solve for t:
40 = -16t^2 + 55t + 50
Rearranging the equation, we get:
16t^2 - 55t + 10 = 0
Now, we can solve this quadratic equation by using the quadratic formula:
t = (-(-55) ± sqrt((-55)^2 - 4*16*10)) / 2*16
t = (55 ± sqrt(3025 - 640)) / 32
t = (55 ± sqrt(2385)) / 32
t ≈ (55 ± 48.83) / 32
So, t can be either:
t ≈ (55 + 48.83) / 32 ≈ 3.76 seconds
t ≈ (55 - 48.83) / 32 ≈ 0.20 seconds
Therefore, it will take the bird approximately 3.76 seconds to reach a height of 40 feet for the first time.