A man with some passengers in his boat, starts perpendicular to flow of river 200 m wide and flowing with `2 m//s.` Speed of boat in still water is `4 m//s.` When he reaches half the width of river the passengers asked him that they want to reach the just opposite end from where they have started.
(a) Find the direction due which he must row to reach the required end.
(b) How many times more time, it would take to that if he would have denied the passengers?

Answer

A, B, C, D

Explanation

(a) `v_(br)=4m//s, v_r=2m//s`
`tan theta=(BC)/(AB)=|v_r|/|v_(br)|=2/4=1/2`


In this case, `v_b` should be along CD.
`:. V_r cos theta=v_(br) sin alpha`

`2(2/sqrt5)=4sin alpha`
or `sin alpha=1/sqrt5`
`:. alpha=theta=tan^-1(1/2)`
(b) `t_1=200/|v_(br)|=200/4=50s`
`DC=DB sec theta=(100)sqrt5/2=50sqrt5m`
`|v_b|=|v_(br)|cos alpha-|v_r|sin theta`
`=4(2/sqrt5)-2(1/sqrt5)=6/sqrt5 m//s`
`:. t_2=(t_1)/2+(DC)/|v_b|=25+(50sqrt5)/(6/sqrt5)=200/3s`
or `(t_2)/(t_1)=4/3`