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and the graph is given by...

Janessa observes Mr Murphy’s “dive” closely enough to form an equation for his height. She finds the equation to be given by:.

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and the graph is given by...

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  1. Janessa observes Mr Murphy’s “dive” closely enough to form an equation for his height. She finds the equation to be given by: • Christopher, Aaron, and Andre, planning a big SI fundraiser, build a 60 meter high-dive platform in the middle of the field. After charging admission for prime bleacher seats, they then “persuade” Mr Murphy to be the first high diver. and the graph is given by...

  2. at 2 seconds? How can we find Mr. Murphy’s velocity at 1 second? when he hits the water? Here is where the slope of the curve plays an important role. h(t) where h represents height off of the ground in meters Note the units here. This is important! t = time in seconds

  3. Remember that we can now find the slope of this curve at any point using the derivative Let’s draw the tangent line at t = 1 second (1, 55.1) h(t) where h represents height off of the ground in meters The derivative is The slope of this line is t = time in seconds

  4. Remember that we can now find the slope of this curve at any point using the derivative Let’s draw the tangent line at t = 1 second (1, 55.1) h(t) where h represents height off of the ground in meters The slope of this line (like any line) is t = time in seconds

  5. or meters per second are the units for Velocity!!! (1, 55.1) h(t) where h represents height off of the ground in meters The slope of this line is So at t = 1 Mr Murphy is falling at a rate of t = time in seconds

  6. at 2 seconds? (2, 40.4) The derivative is h(t) where h represents height off of the ground in meters The slope of this line is So at t = 2 Mr Murphy is falling at a rate of t = time in seconds

  7. at 3 seconds? The derivative is The slope of this line is So at t = 3 Mr Murphy is falling at a rate of (3, 15.9) So what about when he hits the water?

  8. Velocity is the first derivative of position So the lesson here is: What about the second derivative? Acceleration is the second derivative of position (Hint: What are the units on a velocity graph?)

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