How long would it take for an object to fall from the top?

Question

The formula S=16t^2 is used to approximate the distance​ S, in​ feet, that an object falls freely from rest in t seconds. The height of a building is 1487 feet. How long would it take for an object to fall from the​ top?

Answer 1

s=-16t^2 + 1487

16^2 = 1487

t = sqr(1487/256) = about 5.81 seconds to reach the ground

or

s(t) = 16t^2 -1487 = 0

t=5.81 seconds rounded off to 2 decimal places

-16t^2 is the effect of gravity, -32 ft/sec^2 acceleration downward, a negative sign indicating downward.

general formula is

s(t) =-16t^2 + vot + ho where vo=initial velocity, ho = initial height

s'(t) = velocity at time t = v(t) =-32t + vo =-32t if vo=0

when it hits the ground its velocity = -32(1487/256) = 185.88 feet per second

or for the metric system s =-4.9t^2 + vot + h