Solve the Problem $256 \mathrm { ft } / \mathrm { sec }$

Multiple Choice

Solve the problem.
-A professional fireworks team shoots an 8-in. mortar straight upwards from ground level with an initial speed of $256 \mathrm { ft } / \mathrm { sec }$ .
a. Write a function modeling the vertical position $s ( t )$ (in $\mathrm { ft }$ ) of the shell at a time $t$ seconds after launch.
b. The spectators can see the shell rising once it clears a 768-ft tree line. From what period of time after launch is the shell visible?

A) a. $s ( t ) = - 16 t ^ { 2 } + 256 t$
b. The spectators can see the shell between 4 and $12 \mathrm { sec }$ after launch.
B) a. $s ( t ) = - 16 t ^ { 2 } + 256 t + 768$
b. The spectators can see the shell between 4 and $24 \mathrm { sec }$ after launch.
C) a. $s ( t ) = - 32 t ^ { 2 } + 256 t$
b. The spectators can see the shell between 4 and $12 \mathrm { sec }$ after launch.
D) a. $s ( t ) = - 32 t ^ { 2 } + 256 t$
b. The spectators can see the shell between 4 and 24 sec after launch.