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.
To find the time it will take for the bird to reach a height of 40 feet, we need to set the equation equal to 40 and solve for t:
-16t^2 + 55t + 50 = 40
-16t^2 + 55t + 10 = 0
Now, we can use the quadratic formula to solve for t:
t = (-55 ± √(55^2 - 4*(-16)*10)) / 2*(-16)
t = (-55 ± √(3025 + 640)) / -32
t = (-55 ± √3665) / -32
Using a calculator, we find:
t ≈ 0.39 seconds or t ≈ 3.41 seconds
Since we are looking for the time for the bird to reach a height of 40 feet for the first time, we only consider the positive value, which is approximately 3.41 seconds.
Therefore, it will take the bird approximately 3.41 seconds to reach a height of 40 feet in the air for the first time.