# Relative Velocity in 1 Dimension

## Purpose:

• To discover how relative velocities combine.

## Discussion:

Consider Plug and Chug Problem #1 on p. 41 of the text:

"Calculate the resultant velocity of an airplane that normally flies at 200 km/h if it encounters a 50 km/h tailwind. If it encounters a 50 km/h headwind?"

(The problem of combining velocities in one dimension is also discussed in section 3.2 Velocity Vectors, on p. 29 of the text. In particular, see Fig. 3.2)

The phrase "airplane that normally flies at 200 km/h" means that the speedometer of the airplane measures the airplane's speed relative to the surrounding air, so that if there is no wind the airplane's speed relative to the ground will be 200 km/h. Of course, the speed of the wind (air) is measured relative to the ground.

The text says that the answers to the above questions are 250 km/h for the tailwind and 150 km/h for the headwind, which means that:

velocity of plane relative to the ground = velocity of plane relative to the air + velocity of air relative to the ground

where we need to remember that the "+" sign above refers to vector addition.

The question is, does all of this really work? In this lab, you can simulate this situation using a motorized cart to represent the airplane and a large piece of paper to represent the air. The lab table can represent the ground.

## Equipment:

 variable-speed motorized cart meter stick or metric tape stop watch 2 meters of bulletin-board paper

## Procedure:

Design an experiment that will test the text's claim concerning the way velocities add. Some suggested equipment is listed above - you don't have to use all of it, and if you will need additional equipment contact your instructor. Be sure to discuss your plans with your instructor before you begin.

## Questions:

1. A boat is moving downstream (with the current) and its speedometer says 10 km/h. The captain of the boat knows that the current has a velocity of 4 km/h. What is the speed of the boat relative to the river bank? What if the boat turns 180o and goes upstream?
2. An airplane's speedometer indicates that it is moving with a velocity of 120 m/s relative to the air. The compass indicates that the airplane is heading east. If the weather report says that there is a wind blowing toward the east at 30 m/s (relative to the Earth) at the plane's altitude, what is the airplane's velocity relative to the Earth? What would the plane's velocity be if the wind had the same speed toward the west?
3. Suzie is riding in a car moving at 20 m/s (relative to the Earth) when she throws a ball in the same direction that the car is moving. If she can throw a ball at 35 m/s, how fast will the ball be moving (relative to the Earth) when Harry catches it? (Ignore air resistance effects.)

## P.S.:

The relationship between velocities that you have (probably) found is quite simple and logical, isn't it? The amazing thing about it is that it is not true for all velocities! During the last years of the 19th century, experimental physicists, notably Michelson and Morely, were puzzled by results that indicated that the velocity of light did not behave "as it should" with regard to relative velocities. About 1905, Albert Einstein hypothesized that it was a basic fact of nature that all observers, no matter their relative velocity, would always measure the same velocity for light in a vacuum. Imagine that you always measured the same velocity for the cart relative to the table - no matter how fast you pulled the paper! This is a very strange result, which, by the way, only applies to light and other electromagnetic waves. Even though it is very counterintuitive, it has been well confirmed experimentally, many, many times.

last update September 11, 2006 by JL Stanbrough