Question

A boat is moving from the east bank to the west bank on a south 'flowing river. If the speed of the boat is $4\, km/h$ and that of the river is $3\, km/h.$ If the width of the river is $2\, km,$ the distance travelled by the boat is

• A. 5 km
• B. 4 km
• C. 3 km
• D. 2.5 km
• E. 2 km

Answer 1

Answer: (D)

In figure, speed of boat $v_{0}=4\,km / h$, speed of river $v_{r}=3\,km / h$ and width of river $=2\,km$.

The magnitude of the resultant velocity is
$ v_{\text {res }}=\sqrt{v_{b}^{2}+v_{1}^{2}}=\sqrt{3^{2}+4^{2}} $
$\Rightarrow v_{\text {res. }} =5\,km / h$
Since, horizontal component (speed of boat) remain constant, so time taken in travelling $2\, km$ distance is
$t=\frac{2}{4}=0.5\,h$
In $0.5\,h$, distance travelled by object with resultant velocity
$D=v_{\text {res }} \times t=5 \times 0.5=2.5\,km$