How do you calculate the horizontal component of a vector?

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gsenviro eNotes educator| Certified Educator

Vectors are quantities that have both a magnitude and a direction. A common example of a vector quantity is velocity of an object. Unlike speed, velocity is a vector quantity and needs both direction and magnitude for complete description. 

Anything that has a direction can be resolved into its x and y components. For example, when we throw a ball, in a projectile motion, it makes some angle with the horizontal. Knowing that angle and magnitude of velocity, we can resolve the velocity into its x and y components. We can use the basic understanding of trigonometry to do that. 

If the vector with a magnitude, M makes an angle of d degrees with the horizontal, the components of the vector can be calculated as:

Horizontal component = M cos d

Vertical component = M sin d

For example, a projectile thrown with a velocity of 10 m/s at an angle of 60 degrees to the horizontal, will have a horizontal component of

10 cos 60 = 5 m/s.

Hope this helps.

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