Answer:
[tex]t=4s[/tex]
Step-by-step explanation:
The vertical displacement of an object in freefall is given by the next equation:
[tex]\Delta y=y_f-y_i=v_o_y t-\frac{1}{2} gt^2[/tex]
Where:
[tex]y_f=Final\hspace{3}position\\y_i=Initial\hspace{3}position\\t=Time\\g=Standard\hspace{3}gravity\\v_o_y=Initial\hspace{3}velocity\hspace{3}in\hspace{3}y-axis[/tex]
This equation can be reduced to the equation given by the problem since:
[tex]v_o_y=0\\y_f=0\\y_i=s=256\\g\approx 32ft/s^2[/tex]
Hence:
[tex]-s=-\frac{1}{2} 32t^2[/tex]
Solving for t:
[tex]t^2=\frac{256}{16} =16\\\\t=\sqrt{16} =\pm4s[/tex]
Since a negative time wouldn't have sense, the answer is 4 seconds
