Relative velocity

The river is 50 meters wide. The boat is the red circle. Although the boat points in the direction of the red arrow, it will actually travel along the black line, because the water carries the boat downstream. The black line represents the velocity of the boat with respect to the shore. Note that this is the sum of the velocity of the boat with respect to the water (in red) + the velocity of the water with respect to the shore (in blue).

The positive x direction is to the right.
The positive y direction is up.

Here are a few things to think about:

• Adjust the speed of the river. Does it affect the time it takes the boat to cross?
• With the river speed at 2 m/s, can you find a way to make the boat go straight across?
• What determines whether the boat goes upstream, downstream, or straight across?

Created by Andrew Duffy, Boston University Physics Department.

Last update September 9, 1998