Question

Sylvia launches a bottle rocket into the air. The function h(t)= 115t-16t^2 gives the height of the bottle rocket, in feet, 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.

Answer 1

4 seconds to reach 200 feet

Explanation:

You can use Desmos (graphing calculator) then plug in the equation and you will find the x-values are 7.188 and 0- the origin.

Divide 7.188 by 2 (this is also solving for the midpoint/axis of symmetry) and you get 3.594

Round 3.594 to the nearest second which would be 4 seconds.

Hope that helps and have a great day!

Answer 2

It took approximately 2 seconds for the bottle rocket to reach a height of 200 feet.

The height of Sylvia's bottle rocket is modeled by the function h(t)=115t−16t^2, where t represents the time in seconds. To determine the time it took for the bottle rocket to reach a height of 200 feet, we set h(t) equal to 200 and solve for t.

115t−16t^2=200

Rearranging the equation to form a quadratic equation, we get 16t^2−115t+200=0. Solving this quadratic equation provides the values for

t. In this case, the positive root corresponds to the time when the rocket reaches a height of 200 feet. Using a table, graph, or a quadratic formula, we find that t≈2 seconds. Therefore, it took approximately 2 seconds for Sylvia's bottle rocket to reach a height of 200 feet, rounding to the nearest second.