A girl swims at a speed of 4 kmh^-1 in still water. She crossed a river 1km wide that flows steadily at 3kmh^-1. If she travels perpendicular to the river, how far down the river does she go when she reaches the other bank?

option(1)

CONCEPT:

• The displacement is the vector quantity that can be calculated by velocity × time. 
  • Velocity (v) = Displacement/Time 

CALCULATION:

\(\vec {v_m}\) (4kmh^-1) and  \(\vec {v_r}\) (3kmh^-1) represent the velocities of girl and river. 

• Clearly \(\vec {v}\) is the resultant of these velocities. If the girl begins to win along with AB, she will be deflected to the path AC by the flowing river. 

Time taken to cover distance AC with velocity \(\vec {v}\)will be the same as the time taken to cover distance AB with velocity  \(\vec {v_m}\) .

Time taken by the girl to cross the river is:

\(t = \frac {AB}{v_m}= \frac {1km}{4kmh^-1}\)= 1/4.

Distance through which the girl goes down the river is: 

BC = \(\vec {v_r}\)× t = 3 kmh^-1 × 1/4 h = 0.75 km. 

Additional Information

• Vector Quantity is that physical quantity that has both magnitude and direction and obeys the law of vector addition is called vector quantities or vectors.
  • Examples: displacement, velocity, force.