Question

incorrect
your answer is incorrect.

• answer 1: your answer is incorrect.
• answer 2: your answer is incorrect.

a model rocket is launched with an initial upward velocity of 54 m/s. the rockets height h (in meters) after t seconds is given by the following.
h = 54t - 5t²
find all values of t for which the rockets height is 26 meters.
round your answer(s) to the nearest hundredth.
(if there is more than one answer, use the \or\ button.)
your answer

Explanation:

Step1: Set up the equation

Set $h = 26$ in the equation $h=54t - 5t^{2}$, getting $26=54t - 5t^{2}$. Rearrange it to the standard - form of a quadratic equation $5t^{2}-54t + 26 = 0$.

Step2: Identify the coefficients

For the quadratic equation $ax^{2}+bx + c = 0$ (in our case, $x=t$, $a = 5$, $b=-54$, $c = 26$), we use the quadratic formula $t=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$.

Step3: Calculate the discriminant

First, calculate the discriminant $\Delta=b^{2}-4ac=(-54)^{2}-4\times5\times26=2916 - 520 = 2396$.

Step4: Find the values of t

Substitute the values into the quadratic formula:
$t=\frac{54\pm\sqrt{2396}}{10}=\frac{54\pm48.9592}{10}$.
For the plus - sign: $t_1=\frac{54 + 48.9592}{10}=\frac{102.9592}{10}=10.30$ (rounded to the nearest hundredth).
For the minus - sign: $t_2=\frac{54-48.9592}{10}=\frac{5.0408}{10}=0.50$ (rounded to the nearest hundredth).

Answer:

$t = 0.50$ seconds or $t = 10.30$ seconds