Relative Motion

Relative velocity of a passenger on a train with respect to a person on the ground.

Sample Problem

Suppose the passenger on the train is climbing a vertical ladder with a speed of and the train is slowly coasting forward at . Find the speed and direction of the passenger relative to the ground.

Solution:

Find the hypotenuse of the triangle using pythagorean theorem:

Boat Problem Java

Sample Problem

You are riding in a boat going at an angle of 25¾ upstream on a river flowing at . What is your velocity relative to the ground?

Solution:

First break the boat velocity into component vectors:

Then add the vectors in the vertical and horizontal directions:

Then use the pythagorean theorem to find the resultant:

Sample Problem:

In the figure a bat detects an insect (lunch) while the two are flying. The bat has velocity relative to the ground, and the insect has velocity relative to the ground. What is the velocity of the insect relative to the bat, in unit-vector notation and as a magnitude and an angle?

Solution:

or

Then

and

On to Chapter 3