Answer: 1.106 s
Step-by-step explanation:
This situation is related to projectile motion and one the equation that models the height of the blueberry pie in time is:
Where:
is the blueberry pie final height (when it hits the ground)
is the blueberry pie initial height
is the blueberry pie initial velocity
is the angle, assuming the pie was shot horizontally
is the time
is the acceleration due gravity
Rewriting the equation:
Isolating :
Finally:
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Explanation:
The x interval [0,3] is the same as writing
It starts at x = 0 and ends at x = 3.
The graph shows that x = 0 leads to y = 3. So we have the point (0,3) on the parabola. We also have the point (3,-3) on the parabola.
Let's find the slope of the line through these endpoints.
The slope is -2. This is the average rate of change from x = 0 to x = 3.
This is because:
slope = rise/run = (change in y)/(change in x) = average rate of change.
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Now let's find the slope for the table.
Focus on the rows for x = 0 and x = 3. They lead to f(x) = 10 and f(x) = 4 respectively.
We have (0,10) and (3,4) as our two points this time.
We get the same slope as before, so we have the same rate of change.
Notice the change in y (-6) is the same as before. So we could pick any two y values we want as long as there's a gap of 6 between them, and the second y value is smaller than the first.