# Homework Help: Confusion in relative system

1. Oct 1, 2012

### a1231234

1. The problem statement, all variables and given/known data

1)A swimmer wishes to across a swift, straight river of width d. If the speed of the swimmer in still water is u and the speed of the water is v (> u), what is the direction along which the swimmer should proceed such that the downstream distance he has traveled when he reaches the opposite bank is the smallest possible? What is the minimum downstream distance? What is the corresponding time required?

2)As an extension of the last example, if the swimmer wants to cross the swift with a minimum time, find the minimum time and the position that he reaches in the opposite bank.

2. Relevant equations

3. The attempt at a solution
Ans1)The direction along which the swimmer should proceed should be from Q to C
sin∅=u/v AB=d cot ∅ =(d√ 1-(u/v)^2 )/ (u/v) = d√( v^2-u^2)/u
Time taken : t =d / u cos ∅ = d /(1 - (u^2/v^2) )

Problem 1)What confuses me is that t =d / u cos ∅ , isn't that the net velocity of the swimmer equals to the red-line vector ?? Why is it possible to calculate time of travel using part of the velocity ( u cos ∅) ?

Ans2) The minimum time of travel can be obtained if the swimmer directs in the direction of . The magnitude of is contributed completely in the direction of crossing the swift. It is the fastest way. Hence the minimum time t = d/u. The distance downstream s = vt = (vd)/u.

Problem 2) Regardless of the magnitude of u , the total velocity must be affected by the water speed v , which is equals to the red-line vector . why not t= (d/sin∅)/red-line velocity ? For the downstream distance , why is it possible to calculate by multiplying time and part of the total velocity (v ) ?

These confusion has long been troubling me ,so can anyone give me a help ??Thanks very much

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