Graphical Headline April 22, 2002
Space Rail
 The fastest train in the known universe — or the fastest known train in the universe, depending on your perspective — made its inaugural journey last week, 250 miles above Earth's surface. Known as the Mobile Transporter, the train runs on what will eventually be a 300-foot track along the International Space Station. It will be used to ferry the robotic arm that's needed to build onto the space station's outposts.

The Mobile Transporter is a 1-ton, 9-foot-long railcar that moves at less than one inch per second. It earns the title of the universe's fastest train because of the velocity of the International Space Station, which is orbiting Earth at over 17,000 mph. Relative to Earth's surface, the Mobile Transporter is going at a speed that's difficult to fathom, but relative to its own track, the Transporter crawls.

The International Space Station, hundreds of satellites, and plenty of space junk are all part of the high-speed ballet of objects in orbit around our planet. But you don't have to go into orbit to be a speedy space traveler. You're sitting on Spaceship Earth, a huge, geoid-shaped craft that rotates on its axis at 1,041 mph. This spaceship is also traveling around the Sun at a rate of 66,000 miles per hour (or 8.5 miles per second). You are not aware of the velocity because of the size of the planet and because there are no reference points close by (it's a little like flying in a commercial jet at an altitude of 34,000 feet — it's difficult to have a sense of your true speed because there are no reference points near to you). But as an alien sitting in the Andromeda Galaxy would tell you, speed is all a matter of perspective. To that alien, Spaceship Earth is spiraling through space at about 600,000 mph.

Whether in space or on Earth, there are many interesting problems about relative speeds — and combined velocities — that you and your students will enjoy discussing and solving.

Learn About the Problem
Students can begin by working with the following Riverdeep activity from Middle School Gateways. (To use the activity, you need to be a Riverdeep subscriber, or you can get a free 30-day trial.)

  • Energy and Motion: Speed and Velocity
    In this activity, students are introduced to the concept of velocity. They then look at how an outdoor skater's velocity is affected by a headwind and a tailwind — in other words, how combined velocities work. Combined velocities are the focus of the problems below.

Think About the Problem
 With this series of problems, we start in space and work our way down to Earth's surface.

In the International Space Station 250 miles above Earth's surface

  • Roger Clemens has been invited to play baseball on the International Space Station. An astronaut holding a radar gun measures one of Clemens' pitches at 95 mph. The space station is orbiting Earth at a speed of 17,000 mph. Imagine you could see the game from Earth. From your point of view, what speed is Clemens' pitch traveling at?

Commercial jets cruising at 35,000 feet above Earth's surface

  • An Airbus A330 is cruising north at 530 mph. A Boeing 747 is cruising south at 565 mph. They pass by each other at 2 o'clock. To someone sitting in the Boeing, what speed does the Airbus appear to be traveling at? To someone sitting in the Airbus, what is the apparent speed of the Boeing?

A light aircraft 4,000 feet above Earth's surface
This problem expands on the principle demonstrated with the outdoor skater in the Middle School Gateways Speed and Velocity activity. To solve the problem, students will need to understand the concepts of airspeed and groundspeed — two vital measurements in aviation. The wind speed and direction on a given day dictate the relationship between airspeed and groundspeed. On a calm day, they will be the same; on a windy day, they will differ. With a headwind, the plane's progress over ground is impeded (the plane is "pushed back," so to speak), so its groundspeed will be less than its airspeed. With a tailwind, the plane is pushed along, so its groundspeed will exceed its airspeed.

The airspeed indicator in an airplane tells the pilot what the speed of the air is over the wings, but it says nothing about the plane's speed over ground. Pilots of light aircraft must make their own calculations, taking the wind speed and direction into account, to figure out what the groundspeed is.

Ask students the following questions:

  • Suppose you are flying into a strong, direct headwind (a wind from straight ahead) of 15 knots. Your airspeed indicator shows 120 knots. What is your speed over ground?

  • Now, suppose you are flying with a direct tailwind of 12 knots (that is, the wind is traveling in the same direction you are). Your airspeed indicator shows 100 knots. What is your speed over ground?

Students should be able to figure out why it's advantageous to have a tailwind, and a disadvantage to have a headwind. (A tailwind is like getting extra engine power from nature itself. With a headwind, the pilot has to burn more fuel and take more time to get to her destination.)

Down to Earth, on an airport's moving walkway
Have students fill in the table below. They can do their own experiments with a stopwatch to figure out what their walking and running speeds are. (If you'd prefer to supply them with figures, here's a guide: walking slowly = 2.5 mph; walking quickly = 4 mph; running = 7 mph.)

Walkway speed (ft/sec) What you're doing Your velocity relative to walkway (mph) Your velocity relative to ground (mph)
2 Standing    
2 Walking slowly    
2 Walking quickly    
2 Running    
2 Walking slowly against the direction of the walkway    
2 Walking quickly against the direction of the walkway    
2 Running against the direction of the walkway    

Parachuting
 An excellent way to explain relative speeds is to look at some footage of a parachutist when her parachute deploys. When the parachute opens, the parachutist appears to shoot upwards. Is this because she is pulled upwards by the deployed parachute? No: it's because the cameraperson is still falling at the same rate, while the jumper whose parachute has deployed has slowed down. The cameraperson is now going much faster than the parachutist.

You can view some footage to see this in action. (Look for the links to the .mpg files at the bottom of the page.)

The Winds Aloft
 Commercial jets take advantage of the wind patterns at their cruising altitudes to speed them on their way. One example is over the North Atlantic Ocean, where a jet flying from west to east can take advantage of jet stream winds. On the way back, however, the jet will have a headwind to contend with. Read more about this phenomenon in "Boston to Ireland and Back," an article from The Weather Notebook.


Moving Walkways
 To help students understand the concept of their speed relative to the ground rather than to a moving walkway, ask them to think about a person walking alongside the walkway. What would that person have to do to keep up with someone who is standing/walking/running on the walkway? Clearly, the person on the walkway has the advantage because the walkway is giving them extra speed over ground. The person alongside will have to do more work to keep up.

On the airport railway system
This is an adaptation of the classic "fly on a train" problem (it's also similar to the Roger Clemens space baseball problem, above).

  • The high-speed train between terminals travels at 50 miles per hour. A fly inside the train is flying in the same direction at 4.5 miles per hour. How fast is the fly going relative to a person sitting on the train? How fast relative to someone standing on the train platform?

Extending the Problem
 Students may wish to learn more about the Mobile Transporter and the International Space Station. Here are some excellent resources:

Students can also read the Riverdeep Current archive article, "What's it like to meet an astronaut?", which features an interview with Commander William M. Shepherd.

You can try these Riverdeep activities which focus on distance, speed, and time relationships using interactive simulations. The activities are from Algebra Animator, one of the tools in Riverdeep's Tangible Math software. (To use the activities, you need to be a Riverdeep subscriber, or you can get a free 30-day trial. You'll also need the Logal Express plug-in.) Students will manipulate the graphs and equations describing the following scenarios: