Question

A river $200\, m$ wide is flowing at a rate of $3.0 \,m / s$. A boat is sailing at a velocity of $15 \,m / s$ with respect to the water in a direction perpendicular to the river. How far from the point directly opposite to the starting point does the boat reach on the opposite bank?

• A. $25\, m$
• B. $60 \,m$
• C. $40\, m$
• D. $50 \,m$

Answer 1

Answer: (C)

The given situation is shown in the following figure

Velocity of river, $v_{r}=3 \,ms ^{-1}$
Velocity of boat, $v_{b}=15\, ms ^{-1}$
Width of river $=A B=200 \,m$
According to question, we have to calculate distance $B C$.
Time taken by boat to cross the river,
$t=\frac{A B}{v_{b}}=\frac{200}{15}=\frac{40}{3} s$
Since, boat covers horizontal distance $B C$ due to it own velocity.
Hence, $ B C=v_{r} \times t=3 \times \frac{40}{3}=40\, m$