A single velocity has the same effect as two velocities acting together. What is the single velocity called?
A rower points her boat straight at the far bank and rows steadily. She never aims downstream, yet she lands downstream. Something added itself to her rowing.
The boat moves through the water, and the water itself moves over the riverbed. The water or air an object travels through is called the object's medium. The rowboat's medium is the river water; a plane's medium is the air.
For the rowboat: its velocity over the riverbed is its velocity through the water plus the current's velocity.
The two velocities add as vectors, tip to tail, exactly like the tip-to-tail displacement additions earlier in this topic. When they point the same way, they add as plain numbers. At an angle, the sum is the diagonal.
A tour boat crosses a wide river. Which velocity is the tour boat's velocity over the riverbed?
The same sum runs a plane's flight: its velocity over the ground is its velocity through the air plus the wind's velocity.
A hot-air balloon drifts with the wind. Which thing is the balloon's medium?
The sum explains the rower. She aims straight at the far bank; the current adds a downstream velocity; so her velocity over the riverbed points partly downstream. That is why she lands below her aiming point.
A small plane flies through a steady wind. Its instruments give its velocity through the air. What two velocities add to give the plane's velocity over the ground?
Write down the fact:
an object's velocity over the ground is the vector sum of its velocity through its medium and the medium's velocity
The plane's medium is the air.
Its velocity through the air, plus the wind's velocity over the ground.
Owen paddles a canoe straight downstream. He says his speed over the riverbed is his paddling speed through the water plus the current's speed. Is he correct?
Which two velocities add, as vectors, to give a kayak's velocity over the riverbed?
The water of a lake is flowing. Which statement about a motorboat's velocity over the lakebed is true?
A swimmer aims straight at the far bank of a flowing river and never corrects her heading. What happens to her motion over the riverbed?