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)=□

Explanation:

Step1: Recall power - rule for differentiation

If $y = ax^{n}$, then $y^\prime=anx^{n - 1}$, and for a sum $y = u+v+w$, $y^\prime=u^\prime + v^\prime+w^\prime$.

Step2: Differentiate each term of $s(t)=-16t^{2}+64t + 192$

For the first term $u=-16t^{2}$, $u^\prime=-16\times2t=-32t$; for the second term $v = 64t$, $v^\prime=64$; for the third term $w = 192$ (a constant), $w^\prime = 0$.

Step3: Combine the derivatives

$s^\prime(t)=-32t + 64$.

Answer:

$s^\prime(t)=-32t + 64$