A gull wheels over a harbor. One moment its velocity points up and to the right; the next it points down and to the left. The components of those two velocities differ by more than length. They differ in sign.
Keep the convention you have used since Unit 1's number lines: right is the positive horizontal direction, and up is the positive vertical direction.
The gull flies up and to the right. Rightward makes its horizontal component positive. Upward makes its vertical component positive.
Now the same gull flies down and to the right. One direction word changed. Downward makes the vertical component negative; the horizontal component stays positive.
Now the same gull flies down and to the left. The horizontal word changed too. Leftward makes the horizontal component negative.
Now the same gull flies up and to the left. Leftward keeps the horizontal component negative, and upward makes the vertical component positive.
Last, the gull folds its wings and drops straight down. Straight down has no rightward or leftward part at all. So its horizontal component is zero, and its vertical component is negative.
A paraglider's velocity points down and to the right. Right and up are positive. State the sign of each component of the velocity.
The direction has two words: down, and to the right.
Rightward makes the horizontal component positive.
Downward makes the vertical component negative.
The horizontal component is positive; the vertical component is negative.
Now make the read quick. Six movers follow, and each asks the same question: is the named component positive, negative, or zero?
Right and up are positive. A gull climbs up and to the right. Is the horizontal component of its velocity positive, negative, or zero?
Right and up are positive. A squirrel runs down a branch, down and to the left. Is the vertical component of its velocity positive, negative, or zero?
Right and up are positive. A skier glides down and to the left. Is the horizontal component of her velocity positive, negative, or zero?
Right and up are positive. A balloon drifts up and to the left. Is the vertical component of its velocity positive, negative, or zero?
Right and up are positive. A stone falls straight down. Is the horizontal component of its velocity positive, negative, or zero?
Right and up are positive. A hawk soars up and to the left. Is the horizontal component of its velocity positive, negative, or zero?
Right and up are positive. A drone's velocity points up and to the left. Which pair gives the signs of its horizontal and vertical components, in that order?
Right and up are positive. A kite's velocity has a negative horizontal component and a negative vertical component. Which way does the kite move?
Right and up are positive. A diving pelican's velocity has a positive horizontal component and a negative vertical component. Which way does the pelican move?