A swimmer can swim with speed 15 m/sec in still water. He wants to reach at point B as shown in
figure. Speed of river is 10root3 m/s & width of river is 100root3 m. If time taken by man to cross the
river is 40/rootn
Then 20n is :
Answers
20n is 60
Explanation:
Width of river = 100√3 m
Vertical Distance = 100√3 m
Tan 60 = 100√3/ Horizontal Distance
=> Horizontal Distance = 100 m
Time taken = 40/√n
Horizontal Speed = 100 / (40/√n ) = 5√n/2 m/s
Swimmer speed = 15 m/s
Angle = α
15Cosα + 10√3 = 5√n/2
=> 3Cosα + 2√3 = √n/2
=> Cosα +2/√3 = √n/6
=> Cosα = √n/6 - 2/√3
=> Cosα = (√n - 4√3 )/6
15Sinα * 40/√n = 100√3
=> Sinα = √3 √n /6
Cos²α + Sin²α = 1
=> ((√n - 4√3 )/6)² + (√3 √n /6)² = 1
=> n + 48 - 8√(3n) + 3n = 36
=> 4n - 8√(3n) + 12 = 0
=> n - 2√(3n) + 3 = 0
=> ( √n - √3)² = 0
=> √n = √3
=> n = 3
20n = 60
and α = 150 °
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