# How Do I Calculate Resultant Velocity?

Resultant velocity is the vector sum of all given individual velocities. Velocity is a vector because it has both speed and direction. There are many ways to calculate vector sums, such as using a vector addition diagram, but using trigonometry to calculate vector components is usually more efficient.

1. Find the magnitude and angle for each velocity given.

First you want to find the angle between each initial velocity vector and the horizontal axis. This is your angle (theta). The speed given is the magnitude of velocity. Be sure to keep your magnitudes and angles organized.

2. Calculate the x and y components of the individual velocity vectors.

The x component of a vector is parallel to the horizontal axis of a graph. The y component is parallel to the vertical axis. To calculate the magnitude of the x components, x = (speed)*cos(theta) To calculate the magnitude of the y components, y = (speed)*sin(theta)

3. Calculate the x and y components of the resultant velocity

The magnitude of the resultant velocity's x component is the sum of all of the individual x components calculated from the initial velocities given. The magnitude of the resultant velocity's y component is the sum of all of the individual y components calculated from the initial velocities given.

4. Calculate the magnitude and direction of the resultant velocity

Now that the magnitudes of the x and y components of the resultant velocity have been calculated, it is possible to find the total magnitude and direction of the resultant velocity. The magnitude of the resultant velocity (R) is calculated, R = sqrt(x^2 + y^2), where x is the magnitude of the x component and y is the magnitude of the y component. The direction is calculated by finding the angle (theta) between the resultant velocity and the horizontal axis, (theta) = arctan(y/x), where x is the magnitude of the x component and y is the magnitude of the y component.

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