Let's convert the initial height from feet to meters first:
[tex]h=400 ft=121.9 m[/tex]
The object is in free fall, so it is moving by uniformly accelerated motion with constant acceleration [tex]g=9.81 m/s^2[/tex] (gravitational acceleration) from initial height h=121.9 m. Its vertical position at time t is given by
[tex]y(t)=h- \frac{1}{2}gt^2 [/tex]
We want to know how long it will take to reach the ground, therefore we should calculate the time t at which the vertical position y(t) becomes zero:
[tex]0=h- \frac{1}{2}gt^2 [/tex]
rearranging,
[tex]t= \sqrt{ \frac{2h}{g} }= \sqrt{ \frac{2(121.9 m)}{9.81 m/s^2} }=4.98 s [/tex]
