Enter the magnitude of the velocity and the angle into the calculator to determine the horizontal and vertical velocities.

Horizontal and Vertical Velocity Formula

The following equation is used to calculate the horizontal and vertical velocities.

Vx = V * cos (a)
Vy = V * sin (a)
  • Where Vx is the horizontal velocity (m/s)
  • Vy is the vertical velocity (m/s)
  • V is the magnitude of the velocity (m/s)
  • a is the angle of the velocity (degrees)

What are Horizontal and Vertical Velocities?

Definition:

Horizontal and vertical velocities describe a velocity vector’s x and y-components, respectively.

How to Calculate Horizontal and Vertical Velocity?

Example Problem:

The following example outlines the steps and information needed to calculate Horizontal and Vertical Velocity.

First, determine the magnitude of the velocity. In this example, the magnitude of the velocity is found to be 125 m/s.

Next, determine the angle of the velocity. For this problem, the angle is found to be 25 degrees.

Finally, calculate the the Horizontal and Vertical Velocities using the formula above:

Vx = V * cos (a)

Vy = V * sin (a)

Vx = 125 * cos (25deg) = 113.288 m/s

Vy = 125* sin (25deg) = 52.827 m/s

FAQ

What is the significance of calculating horizontal and vertical velocities?

Calculating horizontal and vertical velocities is crucial in physics and engineering to understand the motion of objects in two dimensions. It helps in analyzing projectile motion, determining the range, height, and time of flight of projectiles, and in various applications like ballistics, sports science, and designing trajectories for objects.

Can horizontal and vertical velocities be equal?

Horizontal and vertical velocities can be equal at specific angles of projection in projectile motion, specifically at 45 degrees, where the sine and cosine of the angle are equal, thus giving equal magnitudes for horizontal and vertical components of velocity, assuming the magnitude of the initial velocity is the same in both directions.

How do air resistance and gravity affect horizontal and vertical velocities?

Gravity directly affects the vertical velocity of an object by either increasing it (when the object is falling) or decreasing it (when the object is thrown upwards) over time. Air resistance, on the other hand, acts against the direction of motion, reducing both horizontal and vertical velocities. The effect of air resistance is more pronounced at higher speeds and for objects with larger surface areas.