A `400 m` wide river is flowing at a rate of `2.0 m s^-1`. A boat is sailing with a velocity of `10 m s^-1` with respect to the water, in a direction perpendicular to the river.
(a) Find the time taken by the boat to reach the opposite bank.
(b) How far from the point directly opposite to the starting point does the boat reach the opposite bank ?
( c) In what direction does the boat actually move ?

Answer

A, B, D

Explanation

Here the boat moves with the resultant velocity r, but the vertical component 10 m/s takes him to the opposite shore.
`tan theta = 2/10 = 1/5`
` Velocity = 10 m/s`
`Distance = 400 m`
`Time = 4008/10 = 40 sec`

b. The boat will reach the point C.
In `/_\ABC, tan theta = (BC)/(AB)= (BC)/400= 1/5`
`rarrBC= 400/5=80 m`