Height equation

Question

A stone is dropped from the edge of a roof, and hits the ground with a velocity of -125 feet per second. How high (in feet) is the roof?

Answer 1

v(t) = ∫a(t)dt = ∫-gdt = -∫32dt = -32t + v(0)

 

v(0) = 0 if dropped from rest

 

v(t) = -32t

 

-125 = -32t

 

t = 125/32 sec ≅ 3.91 sec

 

Now plug this value of t into 

 

h = 16t²

 

h = 16(3.91)² ft ≅ 244.61 ft