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Consider the situation of the previous problem. The man has to reach the other shore at the point directly opposite to his starting point. If he reaches the other shore somewhere else, he has to walk down to this point. Find the minimum distance that he has to walk.

Consider the situation of the previous problem. The man has to reach the other shore at the point directly opposite to his starting point. If he reaches the other shore somewhere else, he has to walk down to this point. Find the minimum distance that he has to walk.

Grade:upto college level

1 Answers

Deepak Patra
askIITians Faculty 471 Points
9 years ago
Sol. Velocity of man V ⃗m = 3 km/hr BD horizontal distance for resultant velocity R. X-component of resultant Rx = 5 + 3 cos θ t = 0.5 / 3sinθ which is same for horizontal component of velocity. H = BD = (5 + 3 cos θ) (0.5 / 3 sin θ) = (5+3 cos⁡θ)/(6 sin⁡θ ) For H to be min (dH/dθ) = 0 ⇒ d/(d θ) ((5+3 cos⁡θ)/(6 sin⁡θ )) = 0 ⇒ –18 (sin2 θ + cos2 θ) – 30 cos θ = 0 ⇒ –30 cos θ = 18 θ cos θ = –18 / 30 = –3/5 Sin θ = √(1-cos^2⁡〖θ 〗 ) = 4/5 ∴ H = (5+3 cos⁡θ)/(6 sin⁡θ ) = (5+3 (-3/5))/(6 x (4/5)) = 2/3 km

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