2. Gracie and Vivian, planning a big SI fundraiser (actually it’s just to pay for the food at their table), 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.
Owen and Garo observe Mr Murphy’s “dive” closely enough to form an equation for his height. They find the equation to be given by:
and the graph is given by...

3. Here is where the slope of the curve plays an important role.
How can we find Mr. Murphy’s velocity at 1 second?
at 2 seconds?
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

4. Let’s draw the tangent line at t = 1 second
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

5. Let’s draw the tangent line at t = 1 second
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

6. (1, 55.1) or meters per second are the units for Velocity!!!
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

7. Velocity is the first derivative of position
So the lesson here is:
Apply the Power Rule to dy …
Let’s look at some free fall equations from Physics, shall we?
and you get vfy
Keeping in mind that viy and ay are both constants…
Constants
Velocity
What about the second derivative?
Acceleration

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
What are the units on a velocity graph? or

9. at 2 seconds? (2, 40.4) The derivative is The slope of this line 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

10. So what about when he hits the water?
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?

11. So what about when he hits the water?
The location on the graph at which he hits the water is the x-intercept
So let’s use the calculator to find the exact location of the x-intercept
So what about when he hits the water?
( , 0)

12. So what about when he hits the water?
The derivative is
The slope of this line is
So when he hits the water, Mr Murphy is falling at a rate of
So what about when he hits the water?
( , 0)