Sylvia launches a bottle rocket into the air. The function h(t)=115t−16t2+300 gives the height of the bottle rocket, in feet, t seconds after it is launched. Using a table or graph, about how many seconds did it take for the bottle rocket to reach a height of 200 feet? Round your answer to the nearest second. (1 point) Responses -8 seconds -8 seconds -10 seconds -10 seconds 8 seconds 8 seconds 10 seconds

Question

Sylvia launches a bottle rocket into the air. The function h(t)=115t−16t2+300 gives the height of the bottle rocket, in feet, t seconds after it is launched. Using a table or graph, about how many seconds did it take for the bottle rocket to reach a height of 200 feet? Round your answer to the nearest second. (1 point) Responses -8 seconds -8 seconds -10 seconds -10 seconds 8 seconds 8 seconds 10 seconds

Answer 1

To find out how many seconds it takes for the bottle rocket to reach a height of 200 feet, we need to set the function h(t) equal to 200:

115t−16t^2+300 = 200
-16t^2+115t+100 = 0

We can now solve this quadratic equation to find the two possible times when the height is 200 feet. Using a graphing calculator or other methods, we find that the two solutions are t = 8 seconds and t = 10 seconds.

Therefore, the bottle rocket took between 8 and 10 seconds to reach a height of 200 feet. Rounding to the nearest second, our answer is 8 seconds.