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November 27, 2014

November 27, 2014

Posted by **Elisabeth** on Thursday, July 8, 2010 at 10:32pm.

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?

- Calculus/Physics -
**Quidditch**, Thursday, July 8, 2010 at 11:07pmYou 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

- Calculus/Physics -
**Elisabeth**, Thursday, July 8, 2010 at 11:28pmAssuming 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.

- Calculus/Physics -
**Quidditch**, Friday, July 9, 2010 at 12:12amIn 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.

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