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: Substitute values into formula

$$t = \frac{-144 \pm \sqrt{144^2 - 4(-16)(0)}}{2(-16)}$$

Step4: Simplify the expression

$$t = \frac{-144 \pm 144}{-32}$$

Step5: Calculate two solutions

First solution: $t = \frac{-144 + 144}{-32} = 0$
Second solution: $t = \frac{-144 - 144}{-32} = \frac{-288}{-32} = 9$

Step6: Select valid time

$t=0$ is launch time; valid time is 9 seconds.

Answer:

c. 9 seconds