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a stone is dropped from the edge of a roof, and hits the ground with a velocity of −185 feet per second. assume the acceleration due to gravity is -32 feet per second squared. how high (in feet) is the roof?

The way I solve this problem is through a series of two equations. The equations are

Vf = Vo + gt     (1)

and 

x = Vo*t + 0.5*g*t^2     (2)

where Vf is the final velocity
Vo is the initial velocity (equal to zero)
g is the acceleration due to gravity
t is the time of travel
x is the distance traveled.

The first eqn is used to calculate the time it takes to reach the bottom. Therefore, substituting value to eqn 1, we get

185 = 32*t
t = 5.78 s

The second equation can be used to calculate the height of the roof

x = 0.5*32*5.78^2
x = 534.53 ft

hope this helps