In physics, when you work on velocity problems, you break the motion into two components, vertical and horizontal. You use vertical velocity for problems that include an angle of trajectory. Horizontal velocity becomes important for objects moving in a horizontal direction. The horizontal and vertical components are independent of one another, so any mathematical solution will treat them separately. Generally, horizontal velocity is horizontal displacement divided by time, such as miles per hour or meters per second. Displacement is simply the distance an object has traveled from a starting point.

TL;DR (Too Long; Didn’t Read)

In physics problems involving motion, you treat horizontal and vertical velocities as two separate, independent quantities.

Identifying the Horizontal Velocity

The horizontal velocity of a motion problem deals with motion in the x direction; that is, side to side, not up and down. Gravity, for example, acts only in the vertical direction and doesn’t affect horizontal motion directly. Horizontal velocity comes from forces that act in the x-axis.

Tips for Recognizing Horizontal Velocity

Learning to recognize the horizontal velocity component in a motion problem takes practice. Situations that have horizontal velocity include a ball thrown forward, a cannon firing a cannonball, or a car accelerating on a highway. On the other hand, a rock dropped straight down into a well has no horizontal velocity, only vertical velocity. In some instances, an object will have a combination of horizontal and vertical velocity, such as a cannonball shot at an angle; the cannonball moves both horizontally and vertically. Although gravity acts only in the vertical direction, you may however have an indirect horizontal velocity component, such as when an object rolls down a ramp.

Writing the Horizontal Component

For a general velocity problem you can simply write an equation using “V” for velocity, such as:

(V=atimes t)

However, to write a motion equation that treats horizontal and vertical velocity separately, you must distinguish the two by using Vx and Vy, for horizontal and vertical velocity, respectively. If the problem asks for both horizontal and vertical velocities, you write them as two separate equations, such as these:

(V_x=25times frac{x}{t}text{ and }V_y=-9.8times t)

Solving a Horizontal Velocity Problem

Write the horizontal velocity problem as

(V_x=frac{Delta x}{t})

where Vx is the horizontal velocity. For example:

(V_x=frac{20text{ m}}{5text{ s}}=4text{ m/s})

Divide Displacement by Time

Divide the horizontal displacement by time to find the horizontal velocity. In the example, Vx = 4 meters per second.

Calculating Negative Velocity

Try a more difficult problem, such as:

(V_x=frac{-5text{ m}}{4text{ s}})

In this problem, Vx = -1.25 m/s. A negative horizontal velocity means that the object moved backward from its original position.