So far, two vectors have become one: a 6 m/s east velocity and an 8 m/s north velocity act exactly like one 10 m/s velocity aimed 53° north of east.
The trade also runs backwards: one vector can be swapped for two.
Run the replacement in reverse: the single 10 m/s velocity can be replaced by 6 m/s east plus 8 m/s north. The pair has the same effect. Any vector can be replaced like this: a horizontal piece plus a vertical piece that together have the same effect as the original.
The two replacement vectors are called the original vector's components. The horizontal one is its horizontal component; the vertical one is its vertical component.
Here is one vector: 10 m/s, aimed 37° above the horizontal.
That velocity acts exactly like 8 m/s horizontal plus 6 m/s vertical.
A 20 m/s velocity is replaced by its two components. Which statement must be true?
Horizontal and vertical are perpendicular, so a vector's two components always meet at a right angle.
Alba says: 'A thrown ball's velocity, aimed above the horizontal, can be replaced by a horizontal velocity plus a vertical velocity with the same effect.' Is Alba correct?
Neither component is half of the original. The two sizes are usually different: the vector's direction fixes them.
Kofi says: 'A 12 m/s velocity's components must each be 6 m/s.' Is Kofi correct?
A soccer ball leaves a kick at 26 m/s, aimed above the horizontal. What pair of vectors can replace that velocity with the same effect?
Write down the fact:
any vector can be replaced by a horizontal piece plus a vertical piece with the same effect
Its horizontal component plus its vertical component.
A 15 m/s velocity aimed 20° above the horizontal is replaced by its two components. Acting together, what must the pair do?
Write down the fact:
components are defined by one test: the same effect as the original
Exactly what the original 15 m/s velocity does: the same effect.
Type the name for the two perpendicular vectors that together replace a single vector with the same effect.
A 34 m/s velocity aimed above the horizontal is replaced by its components. Which statement is correct?
Mira replaces a 9 m/s velocity aimed above the horizontal with its two components. Which statement about the components' sizes is correct?
A 25 m/s velocity is aimed 40° above the horizontal. Which pair of vectors could replace it with the same effect?