What is the vertical acceleration of the projectile?

AI Thread Summary
The discussion focuses on calculating the vertical acceleration of a projectile using provided height data points taken every 0.1 seconds. The average velocities between each segment were calculated, resulting in values that indicate downward acceleration, but these values do not match the expected acceleration of around -82 cm/s². The user attempted to derive acceleration from the trend line of the velocity versus time graph but found discrepancies in the results. They are seeking guidance on how to accurately determine the vertical acceleration in cm/s². Clarification on the calculations and methodology for achieving the correct acceleration value is requested.
OblivionMage
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Homework Statement



Find the vertical acceleration of the projectile using the following points of data:

y-axis:

33.37
32.87
31.72
30.02
27.8
24.8
21.05
16.7
11.85
6.5
0.6

each value is 0.10s from each other in the x-axis (a mark is was made on the plot every 0.1s)

I know that the acceleration will slightly lower than -82cm/s/s

*all values in cm

Homework Equations



Vav=d/t

Trend line of a V/t graph should give the acceleration

The Attempt at a Solution




I tried to get the Vav of each segment:

1st)

the Vav between 33.37cm and 32.87cm = d/t:

d = 32.87cm - 33.37cm
d = -0.5cm

t = 0.1s - 0.0s
t = 0.1s

Vav = -0.5cm/0.1s
Vav = -5cm/s

2nd

the Vav between 32.87cm and 31.72 = d/t:

d = 31.72cm - 32.87cm
d = -1.15cm

t = 0.2s - 0.1s
t = 0.1s

Vav = -1.15cm/0.1s
Vav = -11.5cm/s

The full list of values:

-5
-11.5
-17
-22.2
-30
-37.5
-43.5
-48.5
-53.5
-59

*all values in cm/s

the trend line would be:

-32.77cm/s which would somehow equal the acceleration?

It makes sense that the values are accelerating downwards, but they are not doing so quickly enough (as stated above, the acceleration should be around (below) -82cm/s/s).

I'm unsure of what to do next, I know that my acceleration was not cm/s/s, but I'm not sure how I would get there.

Any help is appreciated ;)
 
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EDIT: (a) What is the total distance travelled?d = 33.37cm - 0.6cmd = 32.77cm(b) What is the time taken for the projectile to travel the 32.77cm?t = 32.77cm/Vavt = 32.77cm/-32.77cm/st = 1s
 
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