Question

If an object is dropped, the distance it fails during t seconds is given by d(t)=1/2gt^2, where g is about 32ft/sec^2. Find the distance an object would fall in 8 seconds.

Answer 1

Since the distanc function is given by

$d(t)=\frac{1}{2}gt^2$

in order to find the distance at 8 seconds, we need to substitute t=8 into this function, that is,

$d(8)=\frac{1}{2}g(8)^2$

By taking into account that g=32 ft/sec^2, we have

$d(8)=\frac{1}{2}(32)(64)$

which gives

$\begin{gathered} d(8)=16\times64 \\ d(8)=1024 \end{gathered}$

Therefore, the answer is 1024 ft, which corresponds to the last option.