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A swimmer wishes to cross a 500 m wide river flowing at 5 km/h. His speed with respect to water is 3 km/h. (a) If he heads in a direction making an angle θ with the flow, find the time he takes to cross the river. (b) Find the shortest possible time to cross the river.

A swimmer wishes to cross a 500 m wide river flowing at 5 km/h. His speed with respect to water is 3 km/h. (a) If he heads in a direction making an angle θ with the flow, find the time he takes to cross the river. (b) Find the shortest possible time to cross the river.

Grade:upto college level

3 Answers

Navjyot Kalra
askIITians Faculty 654 Points
7 years ago
Sol. a) The vertical component 3 sin θ takes him to opposite side. Distance = 0.5 km, velocity = 3 sin θ km/h Time = Distance/(Velocity ) = 0.5/(3 sin⁡θ ) hr = 10/sin θ min. b) Here vertical component of velocity i.e. 3 km/hr takes him to opposite side. Time = Distance/Velocity = 0.5/3 = 0.16 hr ∴ 0.16 hr = 60 x 16 = 9.6 = 10 minute.
rohan duseja
15 Points
one year ago
the swimmer wont be able to make it only as the speed of river is more as compare to the swimmer 
he will drown for sure
ankit singh
askIITians Faculty 614 Points
10 months ago

Answer

V=3sinS=0.5KMT=3sin0.5hours=sin10min

Vertical componenet to opposite side =3KM/hr
T=30.5=0.16hr=10min

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