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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).
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)?
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).
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).
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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13.oswin.tsang
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