Idea 6of 6Builds onWhose velocity is itTwo arrows, one path
Across the current
She aims straight across the river. Where does she land?
Today you'll discover
- what the water does to a swimmer who aims straight across
- why the two velocities add at a corner
- where to aim to land straight across
Think firstA swimmer aims straight across a flowing river
She swims straight for the far bank. Where does she reach it?
Decide first, then press Next. Watch the slanted arrow, then watch where she points to land straight across.
A river flowing from left to right with a swimmer on the near bank. After a prediction, an arrow across the river shows her own velocity and an arrow along it shows the current; then one slanted arrow shows the two added, ending downstream on the far bank. A boat then aims upstream so the added arrow runs straight across, and the pointing direction is named. The last step is a plane in a wind from the west.
See the whole ideathe big idea and the key word, in one place
The big idea
The river adds its velocity. Aim upstream: the heading tilts.
See the patternVelocity across the river at 3.0 km/h and a flow of 1.5 km/h add at a right angle to about 3.4 km/h against the shore, slanted downstream. Only the 3.0 across counts toward reaching the far bank: a 100 m river takes two minutes however strong the flow.
Key word
- heading
- the direction a swimmer, boat or plane points itself; its velocity over the ground is the heading's velocity plus the river's or the wind's
About this modelThe arrows are velocities, not paths; the dotted line is where the swimmer actually goes.
The arrows are velocities, not paths; the dotted line is where the swimmer actually goes.
Ready to use it?
- Say where a swimmer or plane ends up for a given heading and current, and which way to aim to go straight.