Question

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?

Answer 1

Vertical velocity of boat $=10m/s$

Width of the river $=400m$

Time taken to cross the river $=\frac{400}{10}=40s$

The river is flowing with a velocity of 2 m/s and the boat has speed 10 m/s perpendicular to the flow of river.

Thus, the resultant of the velocity make an angle $\theta$ such that;

$tan\theta =\frac{2}{10}=\frac{1}{5}$

Thus, the boat will land at a point just opposite to its starting point at distance $x$ which will be given by:

$\frac{1}{5}=\frac{x}{400}x=80m$

Thus, the boat will cross the river in $40s$ at a distance 0f $80m$ directly opposite to the starting point at the opposite shore.