A river 400 m wide is flowing at a rate of 2.0 m/s. A boat is sailing at a velocity of 10 m/s 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?
Given:
Distance between the opposite shore of the river or width of the river = 400 m
Rate of flow of the river = 2.0 m/s
Boat is sailing at the rate of 10 m/s.
The vertical component of velocity 10 m/s takes the boat to the opposite shore. The boat sails at the resultant velocity
.
Time taken by the boat to reach the opposite shore:
From the figure, we have:
The boat will reach point C.
In ∆ABC,
Magnitude of velocity
|
Let 
be the angle made by the boat sailing with respect to the direction of flow.
Distance the boat need to travel to reach the opposite shore =
(b) Using Pythagoras’ theorem, we get:
