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How do you solve for the average velocity given positions and times?

As the clock winds down in the NBA finals, Kobe Bryant dribbles to the 3-point line in the middle of the court, spins, pulls up and shoots the ball. Assume he releases the ball at the same height as the basket, and at a position x = 21 ft relative to the half court line. Also assume that the basket is a position x= 44.75 ft relative to the half court line. If he releases the ball when there are 2.25 seconds left in the game, and the ball goes in with 0.03 seconds left, then what is the average velocity of the ball? Can you figure out the average speed of the ball?

Summary

  1. H- half court
  2. B- basket
  3. sec- seconds
  4. t- time
  5. xref- reference position
  6. x3- 3 point position
  7. xB- position of the basket
  8. vavg- average velocity is unknown

Notes

    1. We are trying to calculate the average velocity
    1. vavg- average velocity
    2. x- position
    3. t- time
    1. ∆ always means final minus initial
    1. vavg- average velocity
    2. x- position
    3. t- time
    4. ft- feet
    5. sec- seconds
    1. vavg- average velocity
    2. ft- feet
    3. sec- seconds
    1. vavg- average velocity
    2. ft- feet
    3. sec- seconds
    1. We are trying to calculate the average speed
    1. savg- average speed
    1. savg- average speed
    2. sec- seconds
    1. The path between the initial and final position could be anything, so the total distance traveled is not known
    1. Without knowing the total distance traveled, we can't hope to know the average speed!