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Question Number 19200 by Tinkutara last updated on 06/Aug/17
A river of width d is flowing with speed  u as shown in the figure. John can swim  with maximum speed v relative to the  river and can cross it in shortest time  T. John starts at A. B is the point  directly opposite to A on the other  bank of the river. If t be the time John  takes to reach the opposite bank, match  the situation in the column I to the  possibilities in column II.  Column I  (A) John reaches to the left of B  (B) John reaches to the right of B  (C) John reaches the point B  (D) John drifts along the bank while  minimizing the time  Column II  (p) t = T  (q) t > T  (r) u < v  (s) u > v
Ariverofwidthdisflowingwithspeeduasshowninthefigure.JohncanswimwithmaximumspeedvrelativetotheriverandcancrossitinshortesttimeT.JohnstartsatA.BisthepointdirectlyoppositetoAontheotherbankoftheriver.IftbethetimeJohntakestoreachtheoppositebank,matchthesituationinthecolumnItothepossibilitiesincolumnII.ColumnI(A)JohnreachestotheleftofB(B)JohnreachestotherightofB(C)JohnreachesthepointB(D)JohndriftsalongthebankwhileminimizingthetimeColumnII(p)t=T(q)t>T(r)u<v(s)u>v
Commented by Tinkutara last updated on 06/Aug/17
Commented by ajfour last updated on 07/Aug/17
Commented by ajfour last updated on 07/Aug/17
To minimise the time, θ=0  and john reaches to the right of B.      t=T=(d/v)  ;  drift=((ud)/v)  regardless of v>u or v<u .  If θ>0 or θ<0 ⇒  t=(d/(vcos θ)) > T  If John reaches left of B,       θ > sin^(−1) ((u/v)) and v>u , t>T  If time is to be minimised, John  shouldn′t waste time drfting  along the bank.  (A)→(q),(r)  (B)→(p) or (q), (r) or (s)  (C)→(q),(r)  (D)→(q),(r) or (s)
Tominimisethetime,θ=0andjohnreachestotherightofB.t=T=dv;drift=udvregardlessofv>uorv<u.Ifθ>0orθ<0t=dvcosθ>TIfJohnreachesleftofB,θ>sin1(uv)andv>u,t>TIftimeistobeminimised,Johnshouldntwastetimedrftingalongthebank.(A)(q),(r)(B)(p)or(q),(r)or(s)(C)(q),(r)(D)(q),(r)or(s)
Commented by Tinkutara last updated on 07/Aug/17
Thank you very much Sir!
ThankyouverymuchSir!ThankyouverymuchSir!
Commented by ajfour last updated on 07/Aug/17
thanks.
thanks.thanks.

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