The Physics
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Opus in profectus

Distance & Displacement

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Problems

practice

  1. A mountain climbing expedition establishes a base camp and two intermediate camps, A and B. Camp A is 11,200 m east of and 3,200 m above base camp. Camp B is 8,400 m east of and 1,700 m higher than Camp A. Determine the displacement between base camp and Camp B.
  2. A laser beam is aimed 15.95° above the horizontal at a mirror 11,648 m away. It glances off the mirror and continues for an additional 8570. m at 11.44° above the horizon until it hits its target. What is the resultant displacement of the beam to the target?
  3. Three of the four busiest airports in the US are Hartsfield-Jackson in Atlanta, Georgia (ATL), O'Hare in Chicago, Illinois (ORD), and Dallas/Fort Worth in Texas (DFW). Complete the following table for roundtrip airplane journey from Atlanta to Chicago to Dallas to Atlanta. Note: Headings are measured clockwise from due north.
    A roundtrip airplane journey
    departure arrival distance heading
    ATL ORD 975 km 342.8°
    ORD DFW 1291 km 221.6°
    DFW ATL  
    round trip   n/a
  4. Calculate both the distance and the magnitude of the displacement of the Earth after…
    1. one complete orbit around the sun
    2. one-half orbit around the sun
    3. one-fourth orbit around the sun
    4. What relationship between distance and displacement does this illustrate?

conceptual

  1. For each of the following questions, decide whether the questioner is asking for the distance or the magnitude of the displacement (or either or neither).
    1. How far do you walk each day?
    2. How far is it from Toronto to Mexico City by airplane?
    3. How far is it from Toronto to Mexico City by car?
    4. How far is the Earth from the moon?
    5. How long is a standard sheet of plywood?
    6. How long is the coastline of Britain?
    7. How long is the Nile?
    8. How long is the track on a compact disc?
    9. How long did it take you to get here?
    10. How many frequent flyer miles do you have?
    11. What is the radius of the Earth?

numerical

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