Answer
273.27 meters
Work Step by Step
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:
$\Delta x = \frac{1}{2}gt^2=\frac{1}{2}(9.81)(7.464)^2=\fbox{273.27 meters}$
