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 $4km/h$ and that of the river is $3km/h.$ If the width of the river is $2km,$ 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 $v_0=4km/h$, speed of river $v_r=3km/h$ and width of river $=2km$.

The magnitude of the resultant velocity is
$v_{\text{res }}=\sqrt{v_b^2+v_1^2}=\sqrt{3^2+4^2}$
$\Rightarrow v_{\text{res. }}=5km/h$
Since, horizontal component (speed of boat) remain constant, so time taken in travelling $2km$ distance is
$t=\frac{2}{4}=0.5h$
In $0.5h$, distance travelled by object with resultant velocity
$D=v_{\text{res }}\times t=5\times 0.5=2.5km$