Modelling with integration/diff. erentation

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13.oswin.tsang
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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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JaredzzC
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You've done fine so far.

Remember your constant of integration.
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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RDKGames
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(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 t seconds is f(t). We are looking to determine what the height is after 3 seconds, therefore we are interested in calculating f(3).

To do that, we first need to know what f(t) is.

To do that, we need to integrate f'(t) under the initial condition that f(0) = 70.

Your solution for f(t) is *not quite* correct because it implies f(0) = 0 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 f(t) = -4.9t^2 + C. We want f(0) = 70 therefore we set f(0) =-4.9(0)^2 + C = 70. Hence the value of C is clear. Rewrite the particular solution now, and finish off the question.
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13.oswin.tsang
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#4
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thank you so much !
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