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

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
failed

Solution

failed
failed

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

This gives us two possible solutions:

_t_₁ = (215 + 200.12) / 32 ≈ 12.97 seconds _t_₂ = (215 - 200.12) / 32 ≈ 0.47 seconds

Final Answer

t = 0.47 seconds or t = 12.97 seconds

Was this solution helpful?
failed
Unhelpful
failed
Helpful