An object is dropped from a tower, 400 ft above the ground. the object's height above ground x seconds after the fall is s(x)equals400minus16xsquared. about how long does it take the object to hit the ground? what is the object's velocity at the moment of impact?

1) 5 s

The vertical position of the object is given by

where

h=400 ft represents the initial height

g = 32 ft/s^2 is the acceleration of gravity

t is the time

We want to find the time t at which the object reaches the ground, so the time t at which

y(t) = 0

By substituting this into the equation, we find

2) 160 ft/s

The object is released from rest, so the initial velocity is zero

u = 0

The final vertical velocity can be found by using

where

v is the final velocity

a = 32 ft/s^2 is the acceleration of gravity

h = 400 ft is the vertical distance covered

Solving for v, we find