Question

Two or more velocities add by ____? Plz help

Answer 1

Two or more velocities are added up by vector addition method.

Further Explanation:

The velocity is a vector quantity. A vector quantity is a unit that required the magnitude as well as the direction for its representation.

The velocity of a body is defined as the rate of change of displacement of the body in a particular direction. Since the velocity consists of the magnitude and the direction both, the simple method of addition cannot be applied for its addition.

The vector addition of the velocities comprise of the resultant magnitude of velocity as the angle made by the resultant.

The resultant magnitude of the velocity is given as:

$\boxed{{v_r} = \sqrt {v_x^2 + v_y^2} }$  

Here, ${v_r}$ is the resultant magnitude and ${v_x}\,\& \,{v_y}$ are the components of velocities in x and y directions.

The angle made by the resultant velocity is given by:

$\boxed{\theta = {{\tan }^{ - 1}}\dfrac{{{v_y}}}{{{v_x}}}}$  

Thus, the addition of two or more velocities takes place by the vector addition method.

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Answer Details:

Grade: High School

Chapter: Vectors and scalars

Subject: Physics

Keywords: Velocities, vectors. Scalar, vector addition, simple addition, magnitude and direction, components, x and y direction.  

Answer 2

By vector addition.
In fact, velocity is a vector, with a magnitude intensity, a direction and a verse, so we can't simply do an algebraic sum of the two (or more velocities). 
First we need to decompose each velocity on both x- and y-axis (if we are on a 2D-plane), then we should do the algebraic sum of all the components on the x- axis and of all the components on the y-axis, to find the resultants on x- and y-axis. And finally, the magnitude of the resultant will be given by
$R= \sqrt{(R_x)^2+(R_y)^2}$
where Rx and Rx are the resultants on x- and y-axis. The direction of the resultant will be given by
$\tan \alpha = \frac{R_y}{R_x}$
where $\alpha$ is its direction with respect to the x-axis.