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