Questions: Initial Knowledge Check
ALEKS - VANESSA LUCERO - Kn
Question 24
A model rocket is launched with an initial upward velocity of 215 ft / s. The rocket's height h (in feet) after t seconds is given by the following.
h=215t-16t^2
Find all values of t for which the rocket's height is 97 feet.
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)
t= seconds
Transcript text: Initial Knowledge Check
ALEKS - VANESSA LUCERO - Kn
Question 24
A model rocket is launched with an initial upward velocity of $215 \mathrm{ft} / \mathrm{s}$. The rocket's height $h$ (in feet) after $t$ seconds is given by the following.
\[
h=215 t-16 t^{2}
\]
Find all values of $t$ for which the rocket's height is 97 feet.
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)
\[
t=\prod \text { seconds }
\]
[lor
ground
Solution
Solution Steps
Step 1: Set up the equation
We are given the height equation _h_ = 215_t_ - 16_t_² and we are asked to find the time _t_ when the height _h_ is 97 feet. So we set the equation equal to 97:
97 = 215_t_ - 16_t_²
Step 2: Rearrange the equation
To solve for _t_, we rearrange the equation into standard quadratic form:
16_t_² - 215_t_ + 97 = 0
Step 3: Solve for _t_ using the quadratic formula
We can solve for _t_ using the quadratic formula:
_t_ = (-b ± sqrt(b² - 4ac)) / 2a
In our equation, a = 16, b = -215, and c = 97. Plugging these values in:
_t_ = (215 ± sqrt((-215)² - 4 * 16 * 97)) / (2 * 16)
_t_ = (215 ± sqrt(46225 - 6176)) / 32
_t_ = (215 ± sqrt(40049)) / 32
_t_ = (215 ± 200.12) / 32