# Modelling with integration/diff. erentation

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#1
I need help with tihs questions. i understand everything in integration but ive always struggled on modelling and how to go around on thinking about the questions.

9) A rock is dropped off a cliff. The height in metres of the rock above the ground after t seconds is given by the function f(t). Given that f(0)=70 and f'(t)=-9.8t, find the height of the rock above the ground after 3 seconds.

From this question, i have concluded only that the height of the cliff is 70m. i have integrated the derivative of f(t) to get -4.9t^2. im not sure if you are supposed to integrate f'(t).
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3 years ago
#2
You've done fine so far.

If at t=0, f(0) = 70 then what's your constant?

Now that you've found the equation relating height and time(from your integration), all you need to do is find what height the rock is at when t=3, i.e. what is f(3)?
Last edited by JaredzzC; 3 years ago
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3 years ago
#3
(Original post by 13.oswin.tsang)
I need help with tihs questions. i understand everything in integration but ive always struggled on modelling and how to go around on thinking about the questions.

9) A rock is dropped off a cliff. The height in metres of the rock above the ground after t seconds is given by the function f(t). Given that f(0)=70 and f'(t)=-9.8t, find the height of the rock above the ground after 3 seconds.

From this question, i have concluded only that the height of the cliff is 70m. i have integrated the derivative of f(t) to get -4.9t^2. im not sure if you are supposed to integrate f'(t).
We are told that the height of the rock from the ground after seconds is . We are looking to determine what the height is after seconds, therefore we are interested in calculating .

To do that, we first need to know what is.

To do that, we need to integrate under the initial condition that .

Your solution for is *not quite* correct because it implies instead. You can fix this by remembering to include the *arbitrary constant of integration* and then finding out what its value must be by imposing the initial condition.

So after integration you should have . We want therefore we set . Hence the value of is clear. Rewrite the particular solution now, and finish off the question.
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#4
thank you so much !
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