## Essential University Physics: Volume 1 (3rd Edition)

Using the known relationships and known equations, we can write the following equation: $x(t-1)-x(t)=-\frac{1}{2}g(t-1)^2+ \frac{1}{2}gt^2$ Using substitution, it follows: $t^2-(t-1)^2=\frac{t^2}{4}$ We now simplify this equation: $t^2-8t+4=0$ Using the quadratic formula, we find: $t=7.464 \ seconds$ Now, we find: $\Delta x = \frac{1}{2}gt^2=\frac{1}{2}(9.81)(7.464)^2=\fbox{273.27 meters}$