The formula h$($t$)=-16$t$2640$t$,$ describes a model rocket's height. h$($t$)$ is the rocket's heightmeasured in feet from the ground, t seconds after take$-$off.$($a$)$ Sketch the graph of ht$)$ for t $0$ using appropriate axes labels.i$.$ Based on the graph of ht$)$ at what times is the rocket at ground level? ii$.$ Explain how you determined the times for part $($i$).$ iii. What is an appropriate domain for ht$)?($b$)$ Find the velocity function vt$)$ of the rocket.i$.$ Sketch the graph of vt$)$ on a separate graph from ht$)$ using appropriate axes labels. ii$.$ Interpret the graph of vt$)$ based on the rocket's actual motion. In other words, what does the graph of vt$)$ tell you about the original function h$($t$)?$iii. Compute the rocket's velocity at t $=0,$ t $=18$ and t $=25.$iv$.$ How do you interpret the signs of the values you obtained from part $($iii$)?$v$.$ What is an appropriate domain for vt$)?($c$)$ Sketch the graph of st$),$ the speed function, on a separate graph from h$($t$)$ and vt$)$ using appropriate axes labels.i$.$ Find the rocket's speed at t $=0,$ t $=18$ and t $=25.$ii$.$ What is an appropriate domain for s$($t$)?($d$)$ After how many seconds will the rocket start falling?i$.$ Justify your answer to part $($d$)$ using what you know about h$($t$)$ and vt$).($e$)$ How long is the rocket in the air?i$.$ What is its velocity at the moment it hits the ground? ii$.$ Why is the velocity at that moment not zero?$($f$)$ Determine the rocket's acceleration, a$($t$).$i$.$ Why does it make sense that a$($t$)$ is constant and negative? Explain. ii$.$ What would happen to the rocket physically if its acceleration was constant andpositive? Explain.iii. What is an appropriate domain for a$($t$)?$