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How do you find the displacement of an object that moves up and down, given initial and final position?

You try to kick a soccer ball in mid air, but miss completely. Instead, your shoe comes flying off, 1 meter above ground, and at a speed of 3 m/s directed straight up. After reaching its peak the shoe eventually ends up hitting you on the head. If you are 1.7 meters tall, then what is the total displacement of the shoe, between when it comes off your foot and when it hits your head?

Summary

  1. y- the variable for vertical position
  2. Remember to define a reference position and direction
  3. yi- initial position
  4. yf- final position

Notes

    1. A "d" with an arrow means displacement
    2. y- vertical position
    3. D- a symbol that means final minus initial
    1. A "d" with an arrow means displacement
    2. m- meters
    3. Plug in the numbers from the diagram to get the answer
    1. A "d" with an arrow means displacement
    2. m- meters
    3. We get positive 0.7 m for the displacement
    1. m- meters
    2. We defined the "up" direction to be positive, so the displacement is an arrow that points up and has a length of 0.7 m
    1. A "d" with an arrow means displacement
    2. y- vertical position
    1. A "d" with an arrow means displacement
    2. m- meters
    3. Now the positions that we plug in are negative numbers
    1. A "d" with an arrow means displacement
    2. m- meters
    3. We get negative 0.7 m for the displacement
    1. m- meters
    2. Here we defined the "up" direction to be NEGATIVE, so the negative displacement is still an arrow that points up and has a length of 0.7 m!
    1. A "d" with an arrow means displacement
    2. m- meters
    3. Regardless of whether we define up to be positive or negative, the displacement is 0.7m pointing UP