Question

the height, h (in feet) of a model rocket launched from the roof of a building at t seconds is given by h = s(t)= - 16(t + 2)(t - 6)
a. expand s(t)= - 16(t + 2)(t - 6) to write it in the form s(t)=at² + bt + c.
s(t)= - 16t² + 64t + 192
b. what is the height of the rocket at t = 0?
the inital height is 192 feet
c. find the formula for the velocity s(t)
s(t)= - 32t + 64
d. what is the initial velocity?
s(0)= ft per sec.

Explanation:

Step1: Recall velocity - time relationship

The velocity function $s^{\prime}(t)$ is the derivative of the position - function $s(t)$. We already know that $s^{\prime}(t)=-32t + 64$.

Step2: Substitute $t = 0$

To find the initial velocity, we substitute $t = 0$ into $s^{\prime}(t)$. So, $s^{\prime}(0)=-32\times0 + 64$.

Step3: Calculate the result

$s^{\prime}(0)=64$.

Answer:

64