Integration word problem (last hw question)

Last question and I'm done! And I'm also stuck, word problems are more of a sore for me than integrals.

1) On the moon the acceleration due to gravity is -1.6 meters per second. A stone is dropped from a cliff on the moon and hits the ground 20 seconds later. How high is the cliff?

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Originally Posted by Hibijibi

Last question and I'm done! And I'm also stuck, word problems are more of a sore for me than integrals.

1) On the moon the acceleration due to gravity is -1.6 meters per second. A stone is dropped from a cliff on the moon and hits the ground 20 seconds later. How high is the cliff?

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Ok there are a bunch of nice physics formulas called the kinematic equations which are great for this stuff, but I'm sure you're supposed to derive it through calculus.

So you start with $\displaystyle a = -1.6\frac{m}{s^2}$ . Integrate that dt and you should get $\displaystyle -1.6t + c_1$. What is C1? It's the initial velocity. You now have a velocity function. Integrate once more and you should get $\displaystyle \frac{-1.6}{2}t^2 + v_{0}t+c_2$. What is C2? That's the initial displacement. You now have a position function. Plug and chug.

How does that look?

Looks like solved. Thanks!