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CBSE Class 11-science Answered

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Asked by smanishkumar2002 | 09 Jun, 2018, 07:54: AM
answered-by-expert Expert Answer
 
Let the distance AD = d. Let the car turn-off highway at C and CD = x
 
Time T to reach from A to B is given by
 
begin mathsize 12px style T space equals space fraction numerator open parentheses d minus x close parentheses over denominator v end fraction plus fraction numerator n cross times square root of x squared plus l squared end root over denominator v end fraction space.................. left parenthesis 1 right parenthesis
end style
where v is speed of car in highway and v/n is spped of car at field and n>1.
Minimum time is obtained by differenting eqn.(1) with respect to x, then equating the derivative to zero,
and get the value of x for minimum T.
 
begin mathsize 12px style fraction numerator d T over denominator d x end fraction space equals space 1 over v open curly brackets negative 1 plus fraction numerator n cross times x over denominator square root of x squared plus l squared end root end fraction close curly brackets space equals space 0 space.............. left parenthesis 2 right parenthesis end style
from eqn.(2) we get begin mathsize 12px style x space equals space fraction numerator l over denominator square root of n squared minus 1 end root end fraction end style
Answered by Thiyagarajan K | 09 Jun, 2018, 01:58: PM
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