Question
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.
Answers
Answered by
GPT 3.5
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.
-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.