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INTEGRATION

INTEGRATION

by REKHA GAUTAM -
Number of replies: 10
CAN ANYONE SOLVE THIS QUESTION Triangle ABC is an equilateral triangle each side being 60 units.At a time t=0,a particle P starts from a and moves along side AC towards C,at a constant rate of 2 units per second,A second particle Q starts from the midpoint of bc with a variable rate so that the area of triangle PQC becomes half of the area of triangle ABC.Determine the time at which Q's rate becomes the same as that of P.
In reply to REKHA GAUTAM

Re: INTEGRATION

by NIKHIL A.Y -

When (60-2t)(30+2t)=1800

i.e. when t=15 units

In reply to NIKHIL A.Y

Re: INTEGRATION

by REKHA GAUTAM -
dear nikhil
good attempt but ur answer is wrong
you havent specified that how did you get the equation
the correct answer is from the equation
(60-2t)(60-2t)=1800


In reply to REKHA GAUTAM

Re: INTEGRATION

by NIKHIL A.Y -

Area of  Triangle PQC=Half of PCxCQxSinC, where PC at any instant t is (60-2t) units and CQ is (30+2t) when Q is moving towards B. Since Q is initially  the midpoint of BC  and Q is moving towards C, the condition of the area will never be satisfied as we know the area of Triangle PQC will be  less than half the area of ABC in that case. So my answer is from the fact that  halfxPCxCQxSinC=halfxhalfxACxCBxSinC.

i.e. PCxCQxSinC= halfx60x60xSinC  => (60-2t)(30+2t)=1800 =>4t2-60t=0

i.e. t=0 or t=15. Hence the answer.

In reply to NIKHIL A.Y

Re: INTEGRATION

by REKHA GAUTAM -
the question clearly states that Q moves at a variable rate
so u cant take CQ as (30+2t) because DQ(where D is the mid-point of BC)is not equal 2t.
it is only at a particular time instant t when the velocity of particle Q becomes 2 units per second
you hav to use the concepts of differentiation and itegration here

In reply to NIKHIL A.Y

Re: INTEGRATION

by Ajay Datta -

Nikhil

I think you got 30+2t wrong as 2t is not the distance covered by Q (towards B) in t sec at variable speed. In fact in my opinion it should be (30+t) if you work it out using V=ft  & S= 12 (ft2) and then apply ft=2 unit/sec  the velocity attained after t sec.

So we get finally 900= 900-t2 which results in t=0 sec only.

That means there is no such situation when the problem (as given) can be accomplished.  

In reply to REKHA GAUTAM

Re: INTEGRATION

by Skanda Prasad -
You havent specified along what direction does Q move, or do we consider a general trajectory, which makes the problem impossible to solve.  
In reply to Skanda Prasad

Re: INTEGRATION

by REKHA GAUTAM -
particle Q is also moving towards point A of triangle ABC
sorry for the error
In reply to REKHA GAUTAM

Re: INTEGRATION

by Ajay Datta -

Dear Rekha Gautam;

You say that Q is moving towards A in that case the area of triangle can never be half of area of ABC. If you draw the diagram you will realise. In fact area of PQC will be approacing to ZERO as time goes on.

In my opinion you want to say "half of area of triangle "AQC" instead of ABC.

In that case there is a problem for which one try for solution.

Confirm if I am correct.