You want to cross a straight river that flows at constant speed of 5.33m/s and i

Question

You want to cross a straight river that flows at constant speed of 5.33m/s and is 127m wide. Your boat has an engine that can generate a speed of 17.5m/s for your boat. Assume that you reach this top speed instantly (so you can neglect the acceleration time). If you want to go directly across the river with a 90o angle relative to the riverbank, at what angle should you point the boat relative to the bank? (b) How long will it take to cross the river this way? (c) In which direction should you aim your boat to achieve minimum crossing time? (d) What is the minimum time to cross the river? Please provide sketches for the two situations, representing the velocity vectors and corresponding angles.

Explanation / Answer

a) in order to go straight , velocity of river should be cancelled.

so component of 17.5 should be equal to 5.33

let x be the angle of boat with river bank

17.5cosx =5.33

x =71.72

b) time to cross river = 127/ (17.5*sin71.72) = 7.64 s

c) in order to rach in minimum time boat should run to its full capacity in straight direction

it means angle of boat with river bank will be 90

d) time taken =127/17.5 = 7.25 s

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