A motorized canoe is pointed [N20degreesW] in a river. If has the capability to move at 5 m/s and filmed moving at 7.6 m/s, what is the velocity of the river?
To find the velocity of the river, we first need to understand and apply the concept of vector addition.
When a motorized canoe moves in a river, its velocity consists of two components: the velocity of the boat itself and the velocity of the river. We can say that the resultant velocity of the boat is equal to the vector sum of these two velocities.
Let's break down the given information:
1. The motorized canoe is moving at a speed of 7.6 m/s. This speed is the magnitude of the resultant velocity of the boat.
2. The motorized canoe is pointed [N20degreesW]. This direction represents the direction of its resultant velocity. In this case, it means that the boat is moving 20 degrees west of north.
Now, let's use trigonometry to determine the components of the boat's velocity:
1. The north component of the boat's velocity can be calculated by multiplying the boat's speed by the cosine of the direction angle: Velocity_north = 7.6 m/s * cos(20).
2. The west component of the boat's velocity can be calculated by multiplying the boat's speed by the sine of the direction angle: Velocity_west = 7.6 m/s * sin(20).
Now that we have the components of the boat's velocity, we can determine the velocity of the river by subtracting the boat's velocity components from the measured velocity of the boat:
River_velocity_north = 0 m/s - Velocity_north.
River_velocity_west = 0 m/s - Velocity_west.
By performing these calculations, you can determine the velocity of the river.