Question

A 400-m wide river is flowing at a rate of $2.0m{s}^{-1}$. A boat is sailing with a velocity of $10m{s}^{-1}$ 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 1

a.) Time taken to cross the river

$t=\frac{d}{v_y}=\frac{400m}{10m{s}^{-1}}=40s$

b. Drift $\left(x\right)=\left(vx\right)\left(r\right)=\left(2m{s}^{-1}\right)\left(40s\right)=80m$

c. Actual direction of boat,

$\theta ={\tan }^{-1}\left(\frac{10}{2}\right)={\tan }^{-1}5.$

(downstream) with the river flow.