Question

for his schools science fair, brad made a bottle rocket powered by the pressure of the carbonated soda in the bottle. he launches the rocket, and it runs out of soda at a height of 9 meters. at that moment, the rocket is moving upward with a velocity of 7 meters per second. it continues to travel upward before falling to the ground. to the nearest tenth of a second, how long does it take the rocket to hit the ground after running out of soda? hint: use the formula h = -4.9t² + vt + s.

Explanation:

Step1: Set up equation

$0 = -4.9t^2 + 7t + 9$

Step2: Identify coefficients

$a=-4.9$, $b=7$, $c=9$

Step3: Calculate discriminant

$\Delta = 7^2 - 4(-4.9)(9) = 49 + 176.4 = 225.4$

Step4: Solve quadratic formula

$t = \frac{-7 \pm \sqrt{225.4}}{2(-4.9)}$

Step5: Compute positive root

$t \approx \frac{-7 - 15.01}{-9.8} \approx 2.2$

Answer:

2.2 seconds