In a video game, a bird is flung on a sling shot and follows a parabolic pathThe path of the bird can be modeled by the equation h = - 16t ^ 2 + 55t + 50 where is the height of the bird 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? 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 solve the equation h = -16t^2 + 55t + 50 for h = 40.
40 = -16t^2 + 55t + 50
-16t^2 + 55t + 50 - 40 = 0
-16t^2 + 55t + 10 = 0
Next, we can use the quadratic formula to solve for t:
t = (-b ± √(b^2 - 4ac)) / 2a
t = (-55 ± √(55^2 - 4(-16)(10))) / (2(-16))
t = (-55 ± √(3025 + 640)) / -32
t = (-55 ± √3665) / -32
t ≈ (-55 ± 60.56) / -32
Now we can calculate the two possible values for t:
t_1 ≈ (-55 + 60.56) / -32 ≈ 0.18
t_2 ≈ (-55 - 60.56) / -32 ≈ 3.86
Since time cannot be negative, the bird will reach a height of 40 feet for the first time approximately 0.18 seconds after being launched.