A river is flowing towards east with velocity of `5m s^(-1)` . The boat velocity is `10m s^(-1)` . The boat crosses the river by shortest path. Hence,

Options

A. The initial direction of rowing of boat is at an angle of` 53^(@)` with upstream direction
B. Time taken to reach the middle of river is 50 seconds
C. After the wind starts blowing, the direction of rowing of boat is `37^(@)` with upstream direction
D. Total time taken by the boat to cross the river along the shortest path is 100 seconds

Answer

abcd

Explanation

Initially
time taken to reach middle of river `=(200)/(v_(SR) sin theta_(1))=(200)/(5(4/5))=50 sec`

after wind starts to blow
`V_(BR) cos theta_(2)=V_(R )+V_(W) cos 45^(@)`
further time taken to reach the other bank
`=(20)/(V_(BR) sin theta_(2) +V_(W) sin 45^(@))=(200)/(5)(5)/(5)+sqrt(2)(1)/(sqrt(2))=200/4 =50 sec therefore` total time taken =100 sec