15,625 feet and either 56.469 seconds or 87.719 seconds
Step-by-step explanation:
strap in because we need calculus buddy. we're given the displacement equation but we want velocity because at the bullets max height it will pause briefly before coming down and this implies zero velocity. derivative of that equation is -32t+1000. set this equal to zero and find t to see how long this takes. 31.25 seconds to reach zero velocity (the tip of the parabolic motion). now plug that t back into the displacement equation to find height after 31.25 seconds and it's like 15,625 which is ridiculously high. now it has to come down so gravity will be taking over here so it has it's own special equations and we know the equation for that is like x=1/2at^2 or something. we know x is 15,625. let's find time it takes to get down by solving that for t. 15,625÷4.9=t^2 so t=56.469 or something. now its unclear if they want the entire time elapsed from firing the gun or just the falling to ground time so if it's the entire time let's go ahead and add that initial 31.25 seconds to the 56.498 seconds so like 87.719 total seconds.
