Sketch the components

A 20 m/s velocity is replaced by its two components. Which statement must be true?

A soccer ball leaves a boot at 10 m/s, aimed 30° above the horizontal. Part of that velocity carries the ball forward. Part of it lifts the ball upward. One slanted arrow is doing two jobs at once.

The ball's velocity on its own: one slanted arrow, two jobs.

In the last lesson you saw that any vector can be replaced by a horizontal component and a vertical component with the same effect. This lesson shows how to draw the two components.

Start with the vector itself: one arrow, 10 m/s long on your scale, aimed 30° above the horizontal.

From the vector's tail, draw a horizontal arrow along the ground direction. End it directly below the vector's tip. This arrow is the horizontal component.

From the tip of the horizontal arrow, draw a vertical arrow up to the vector's tip. This arrow is the vertical component.

The components drawn in: the horizontal leg starts at the vector's tail, and the vertical leg closes the triangle at the tip.

The three arrows now form a right triangle. The two components are its legs, and the legs meet at 90°. The vector itself is the hypotenuse, the longest side.

A sketch resolves an 18 m/s velocity aimed 50° above the horizontal into components. Which arrow is the triangle's hypotenuse?

In a component sketch, the two components meet at what angle?

The sketch must tell the truth about the angle. A vector aimed 30° above the horizontal has a horizontal component longer than its vertical component. A steeper vector, aimed above 45°, has the longer vertical component.

The construction in one line: the horizontal component runs from the vector's tail and ends directly below the tip; the vertical component rises from that point to the tip; the vector itself is the hypotenuse. Label the angle at the tail, the magnitude on the hypotenuse, and each component's name on its leg.

Describe the component sketch of a hang glider's 24 m/s velocity, aimed 55° above the horizontal.

Draw the velocity first:

one arrow, 24 m/s on the scale, at 55° above the horizontal

Draw the horizontal component:

from the arrow's tail, ending directly below the tip

Draw the vertical component:

from that point, up to the tip

Check the proportions: 55° is above 45°, so the vertical leg is drawn longer than the horizontal leg.

A right triangle: the 24 m/s velocity as hypotenuse, a shorter horizontal leg, a longer vertical leg.

Selma sketches the components of a 15 m/s velocity aimed 40° above the horizontal. She says the two components and the velocity arrow form a right triangle, and the velocity arrow is the longest side. Is she correct?

Your turn

A sketch shows a delivery drone's 12 m/s velocity, aimed 65° above the horizontal, as the hypotenuse of a right triangle. One leg lies parallel to the ground. What does the other leg show?

In a correct component sketch of a vector, where does the horizontal component begin?

A velocity is aimed 60° above the horizontal. In a correct component sketch, which statement about the two components is true?