Sylvia launches a bottle rocket into the air. The function h(t)=115t−16t^2+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.

A. -10 seconds

B. -8 seconds

C. 10 seconds

D. 8 seconds

1 answer

To find out how many seconds it took for the bottle rocket to reach a height of 200 feet, we can set up the equation:

115t - 16t^2 + 300 = 200

Simplifying the equation, we get:

-16t^2 + 115t + 100 = 0

We can then use the quadratic formula to solve for t:

t = (-115 ± √(115^2 - 4(-16)(100))) / (2(-16))

t = (-115 ± √(13225 + 6400)) / (-32)

t = (-115 ± √19625) / -32

t = (-115 ± 140) / -32

This gives us two solutions: t = (25/16) or t = -15.625

Since we are looking for a positive value for time, the bottle rocket reached a height of 200 feet approximately 10 seconds after it was launched.

Therefore, the answer is:

C. 10 seconds