What is the vertical acceleration of the projectile?

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SUMMARY

The vertical acceleration of the projectile is calculated using the average velocity (Vav) derived from sequential position data points. The average velocities between each segment were computed, resulting in values ranging from -5 cm/s to -59 cm/s. The trend line of these velocities indicates an acceleration of approximately -32.77 cm/s², which is significantly lower than the expected value of -82 cm/s². The discrepancy suggests that the calculated acceleration does not align with the expected physics of the projectile's motion.

PREREQUISITES
  • Understanding of kinematic equations, specifically Vav = d/t.
  • Familiarity with graphing techniques, particularly trend lines in velocity-time graphs.
  • Basic knowledge of projectile motion principles.
  • Ability to perform calculations involving average velocity and acceleration.
NEXT STEPS
  • Investigate the principles of projectile motion to understand expected acceleration values.
  • Learn how to derive acceleration from a velocity-time graph using linear regression techniques.
  • Study the effects of air resistance on projectile motion to comprehend discrepancies in expected results.
  • Explore advanced kinematic equations to refine calculations of acceleration in vertical motion.
USEFUL FOR

Students studying physics, particularly those focusing on kinematics and projectile motion, as well as educators seeking to clarify concepts related to vertical acceleration and average velocity calculations.

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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