![\bf \textit{initial velocity}\\\\h(t) = -16t^2+v_ot+h_o \qquad \text{in feet}\\\\ v_o=\textit{initial velocity of the object}\\ h_o=\textit{initial height of the object}\\ h=\textit{height of the object at "t" seconds}](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Binitial%20velocity%7D%5C%5C%5C%5Ch%28t%29%20%3D%20-16t%5E2%2Bv_ot%2Bh_o%20%5Cqquad%20%5Ctext%7Bin%20feet%7D%5C%5C%5C%5C%0Av_o%3D%5Ctextit%7Binitial%20velocity%20of%20the%20object%7D%5C%5C%0Ah_o%3D%5Ctextit%7Binitial%20height%20of%20the%20object%7D%5C%5C%0Ah%3D%5Ctextit%7Bheight%20of%20the%20object%20at%20%22t%22%20seconds%7D)
now, we know the cannon is on the ground, thus hₒ is 0
we also know the -16, in case you're wondering, that's the gravity acceleration in feet divided by 2
what we dunno is vₒ, or the initial velocity
however, let's use those values given
![\bf \begin{cases} t=1\\ h(t)=243 \end{cases}\implies 243=-16(1)^2+v_o(1)+0 \\\\\\ 243=-16+v_o\implies \boxed{259=v_o}\\\\ -----------------------------\\\\ \begin{cases} t=2\\ h(t)=452 \end{cases}\implies 452=-16(2)^2+v_o(2)+0 \\\\\\ 452=-64+2v_o\implies \cfrac{516}{2}=v_o\implies \boxed{258=v_o}](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Bcases%7D%0At%3D1%5C%5C%0Ah%28t%29%3D243%0A%5Cend%7Bcases%7D%5Cimplies%20243%3D-16%281%29%5E2%2Bv_o%281%29%2B0%0A%5C%5C%5C%5C%5C%5C%0A243%3D-16%2Bv_o%5Cimplies%20%5Cboxed%7B259%3Dv_o%7D%5C%5C%5C%5C%0A-----------------------------%5C%5C%5C%5C%0A%5Cbegin%7Bcases%7D%0At%3D2%5C%5C%0Ah%28t%29%3D452%0A%5Cend%7Bcases%7D%5Cimplies%20452%3D-16%282%29%5E2%2Bv_o%282%29%2B0%0A%5C%5C%5C%5C%5C%5C%0A452%3D-64%2B2v_o%5Cimplies%20%5Ccfrac%7B516%7D%7B2%7D%3Dv_o%5Cimplies%20%5Cboxed%7B258%3Dv_o%7D)
so, with every passing second, the initial velocity is dropping by 1 foot
after 1 it was 259, then after 2 seconds it became 258
if that continues, after 5 seconds, it'll be 255
so, now if we make t=5 and vₒ=255
then we end up with