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 out when the bird will reach a height of 40 feet, we need to set the equation h=-16t^2 +55t +50 equal to 40 and solve for t:
-16t^2 +55t +50 = 40
-16t^2 +55t +10 = 0
Now, we can solve this quadratic equation using the quadratic formula:
t = (-55 ± sqrt(55^2 - 4(-16)(10))) / 2(-16)
t = (-55 ± sqrt(3025 + 640)) / -32
t = (-55 ± sqrt(3665)) / -32
t = (-55 ± 60.5) / -32
Now we have two potential solutions for t:
t = (-55 + 60.5) / -32 = 5.5 / -32 ≈ -0.17 seconds
t = (-55 - 60.5) / -32 = -115.5 / -32 ≈ 3.61 seconds
Since time cannot be negative, the bird will reach a height of 40 feet for the first time at approximately 3.61 seconds.