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?
To find the time it takes for the bird to reach a height of 40 feet, we can set h equal to 40 in the equation:
40 = -16t² + 55t + 50
Rearranging the equation, we get:
16t² - 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 ± √2385) / 32
Since we are looking for the time it takes for the bird to reach a height of 40 feet for the first time, we will take the positive solution:
t = (55 + √2385) / 32 ≈ 4.77 seconds
Therefore, it will take the bird approximately 4.77 seconds to reach a height of 40 feet in the air for the first time.