To find the resultant velocity of the boat, we can use vector addition since we have velocities in different directions.
Given: Speed of the boat (Vboat) = 3 m/s in the north direction. Speed of the water current (Vcurrent) = 1 m/s in the east direction.
To determine the resultant velocity, we need to find the vector sum of the boat's velocity and the water current's velocity.
Let's represent the north direction as positive y and the east direction as positive x.
The velocity of the boat (Vboat) can be represented as Vboat = 3 m/s in the +y direction.
The velocity of the water current (Vcurrent) can be represented as Vcurrent = 1 m/s in the +x direction.
To find the resultant velocity (Vresultant), we can use the Pythagorean theorem:
Vresultant = sqrt(Vx^2 + Vy^2)
where Vx represents the vector sum of velocities in the x direction and Vy represents the vector sum of velocities in the y direction.
Vx = Vcurrent = 1 m/s Vy = Vboat = 3 m/s
Substituting these values into the equation:
Vresultant = sqrt((1 m/s)^2 + (3 m/s)^2) Vresultant = sqrt(1 m^2/s^2 + 9 m^2/s^2) Vresultant = sqrt(10 m^2/s^2) Vresultant ≈ 3.16 m/s
Therefore, the resultant velocity of the boat, when rowed with a speed of 3 m/s in the north direction and encountering a water current flowing at 1 m/s in the east direction, is approximately 3.16 m/s. The resultant velocity is in the north-east direction.