Two Dimensional Kinematics Projectile Motion

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SUMMARY

The discussion focuses on solving a projectile motion lab involving two-dimensional kinematics. The participant has derived three key equations from their graphs: Y vs. X, X vs. T, and Y vs. T, with specific slopes indicating relationships between variables. The challenge lies in calculating the vertical acceleration (ay) and initial vertical velocity (v0y) using the provided equations, particularly y(t) = -505.11t² + 328.29t + 3.5949. The participant seeks guidance on extracting these values to ultimately determine the launch angle.

PREREQUISITES
  • Understanding of projectile motion principles
  • Familiarity with kinematic equations
  • Ability to interpret graphical data
  • Knowledge of calculus for solving quadratic equations
NEXT STEPS
  • Calculate vertical acceleration (ay) using the second derivative of y(t)
  • Determine initial vertical velocity (v0y) from the y(t) equation
  • Explore the relationship between time and projectile motion variables
  • Research methods for graphically analyzing kinematic data
USEFUL FOR

Students and educators in physics, particularly those focusing on kinematics and projectile motion analysis, as well as anyone involved in experimental physics labs.

Jetsgirl
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Homework Statement



Hi, I am doing a projectile motion lab for two dimensional kinematics. After completing the procedure of the lab, I have 3 graphs where

Y vs. X has a slope of y = -0.0037x2 + 0.9169x + 0.2684


X vs. T has a slope of y = 373.95x + 3.4011


Y vs. T has a slope of y = -505.11x2 + 328.29x + 3.5949

From the graphs, I have to figure out

ay (cm/s^2)
vx (cm/s)
v0y (cm/s)
angle (degrees)




Homework Equations



ax (t) = 0
ay (t) = -g
vx (t) = v0x
vy (t) = voy + ayt

x(t) = x0+v0xt
y(t) = y0+v0yt+1/2ayt^2

Change in angle = (vy^2*change in vs^2 + vx^2 + change in vy^2)/(vx^2 + vy^2) * (180/pi)

The Attempt at a Solution



vx = 373.95 +/- 3.4011

But for voy, and ay, the equations say that I need to use a specific time to find the answer, which I do not have according to the graphs.

Any suggestions on how to obtain the other two (ay, v0y) would be greatly appreciated.
From there I know I can find the angle by plugging all the components into the "change in angle" equation given above.

Thanks all.
 
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You gave the equation for y(t):
y(t) = y_0+v_{y0}t+\frac{1}{2}a_y t^2
You also said that the equation you found for y(t) was (I assumed those should have been 't's not 'x's):
y = -505.11t^2 + 328.29t + 3.5949
So how can you find v0y and ay?
 

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