Question

value: 4
the equation $-16t^{2}+144t$ gives the height, in feet, of a toy rocket t seconds after it was launched up into the air. how long will it take for the rocket to return to the ground? solve the quadratic equation $-16t^{2}+144t = 0$ using the quadratic formula.
a. 7.5 seconds
b. 10.5 seconds
c. 9 seconds
d. 11.5 seconds

Explanation:

Step1: Identify quadratic coefficients

For $-16t^2 + 144t = 0$, $a=-16$, $b=144$, $c=0$

Step2: Recall quadratic formula

$$t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

Step3: Compute discriminant

$\sqrt{b^2 - 4ac} = \sqrt{144^2 - 4(-16)(0)} = 144$

Step4: Calculate two solutions

$t_1 = \frac{-144 + 144}{2(-16)} = 0$
$t_2 = \frac{-144 - 144}{2(-16)} = \frac{-288}{-32} = 9$

Step5: Select valid time

$t=9$ is when rocket returns to ground.

Answer:

c. 9 seconds