How 9 Cheenta students ranked in top 100 in ISI and CMI Entrances?
Learn More

Relative Velocity of Canoe in River

A canoe has a velocity of 0.40m/s southeast relative to the earth. The canoe is on a river that is flowing 0.50m/s east relative to the earth. Find the velocity (magnitude and direction ) of the canoe relative to the river.


We apply the relative velocity relation. The relative velocities are (\vec{v_{CE}}), the canoe relative to the earth, (\vec{v_{RE}}), the velocity of the river with respect to Earth and (\vec{v_{CR}}), the velocity of the canoe relative to the earth.
Hence $$
The velocity components of (
\vec{v_{CR}}) are $$ -0.5+\frac{0.4}{\sqrt{2}}=-0.217m/s$$( in the east direction)
Now, for the velocity component in the south direction
$$ \frac{0.4}{\sqrt{2}}=0.28$$ (in the south direction)
Now, the magnitude of the velocity of canoe relative to river $$ \sqrt{(-0.217)^2+(0.28)^2}=0.356m/s$$
If we consider (\theta) as the angle between the canoe and the river,the direction of the canoe with respect to the river can be given by
$$ \theta=52.5^\circ$$ ( in south west direction)

Knowledge Partner

Cheenta is a knowledge partner of Aditya Birla Education Academy

Cheenta Academy

Aditya Birla Education Academy

Aditya Birla Education Academy

Cheenta. Passion for Mathematics

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.