Calculus/Physics
posted by Elisabeth .
A stone is thrown from a cliff top with an upward velocity of 20 m/s. It takes 7 seconds for the stone to hit the ground at the bottom of the cliff. How high is the cliff?
I know you use the equation of motion
S(t)= (So)+(Vo)t(1/2)gt^2
S(20)= (So) + 140  240.1
(So) = 100.1 m (I know it is supposed to be a positive number)
But doesn't that give you the total height? How do I get rid of the height of the parabola above the cliff?

You have the right formula.
Let S0 be the height of the cliff in meters.
When the stone stops it is at 0m height.
So,
0m = S0 + (v0)t + (1/2)gt^2
t =7 s
g=9.8m/(s^2)
0 = S0 + (20m/s)(7s) + (1/2)(9.8m/(s^2))(49s^2)
0 = S0 + 140m  240.1m
S0 = 100.1m 
Assuming that from the bottom to the top of the cliff is h1 and the top of cliff to the top of the parabola is h2... isn't the 100.1m really h1 + h2 (since the stone is thrown upwards)? I am looking for just h1.

In the equation
s(t) = (s0) + (v0)t + (1/2)(a)(t^2)
s(t) gives the height for some time t.
s0 is the initial height, which is the height of the cliff.
v0 is the initial velocity, for this problem 20m/s. The last term is the distance due to gravity. As t^2 increases, this term finally overwhelms the others and the stone reverses direction and falls back to a point at the base of the cliff.
How high the stone travels above the cliff can be calculated, but it is not needed to find the height of the cliff.