A river 400m wide is flowing at the rate of 2 m/s.A boat is sailing at the rate of 10m/s with repect 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?

 

solution : 

The component of the resultant velocity which is responsible for causing the boat to cross the river has magnitude 10m/s.

 

So time taken to cross the river is 400/10=40s.

 

Now the horizontal displacement of the boat is caused by the velocity of river

 

Distance from point directly opposite to the point from where boat started

  = 40 x 2 =80m

 

u can use vector method also. For example :

 

if u be the velocity of river,& u' be the velocity of boat,

then the net velocity of boat = u i + u' j = 2 i  + 10 j

now the time taken for boat to cross the river,

= ditance / velocity in y-direction 

= 400/ u'

= 40 sec

 

distance travelled by boat in horizontal direction, will be purely due to the river's velocity, thrfore drift  

= u X t

= 2 X 40

= 80 m