a cannon fires a shell that rise (h) cm after t seconds where
$\displaystyle h(t)=800t-16t^2$
how would i find the maximium height (k) reached by the shell and how would its graph look. for $\displaystyle h=800t -16t^2$
a cannon fires a shell that rise (h) cm after t seconds where
$\displaystyle h(t)=800t-16t^2$
how would i find the maximium height (k) reached by the shell and how would its graph look. for $\displaystyle h=800t -16t^2$
$\displaystyle h(t) = 800t - 16t^2$
$\displaystyle h(t) = 16t(50 - t)$
$\displaystyle 0 = 16t(50-t)$
note that the $\displaystyle h = 0$ at $\displaystyle t = 0$ and $\displaystyle t = 50$
due to the parabola's symmetry, the shell will be at its highest point at $\displaystyle t = 25$, midtime between the zeros.
$\displaystyle h(25) = 16(25)[50-25] = 16 \cdot 25^2 = 10000$
$\displaystyle x = ut+\frac{1}{2}at^2$
$\displaystyle \frac{dx}{dt}= v = u+at$
so we have $\displaystyle x=800t-16t^2$
$\displaystyle
\frac{dx}{dt}= v = 800-32t$
when $\displaystyle v=0$ it reaches max. height because when v is negative, it will start falling.
so $\displaystyle \rightarrow 800-32t=0$
rearrange to find t which reaches max height.
which comes to 25s.
then sub it into $\displaystyle x=800t-16t^2$, to find max height.
which comes to 10000m.