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)=(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)=(1)/(2)g(8)^2`

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

`d(8)=(1)/(2)(32)(64)`

which gives

`\begin{gathered} d(8)=16*64 \\ d(8)=1024 \end{gathered}`

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