Bouncing Ball Graph/Quadratic Formula

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Homework Help Overview

The discussion revolves around interpreting the parameters of a quadratic equation derived from the motion of a bouncing ball, as observed through a motion sensor. The subject area includes kinematics and the application of the quadratic formula in the context of projectile motion.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the relationships between the parameters A, B, and C in the equation Y=At^2+Bt+C, questioning the meaning of each in relation to the motion of the ball. There is confusion regarding the negative value of C and how A relates to gravitational acceleration.

Discussion Status

Some participants have provided guidance on the relationship between A and gravitational acceleration, suggesting that A is half of the gravitational acceleration. However, there remains confusion about the implications of the graph and the behavior of the parameters.

Contextual Notes

Participants are working under the constraints of interpreting a specific graph of a bouncing ball, which may influence their understanding of the parameters involved. The discussion includes clarifications about the effects of gravity on the motion described by the equations.

Megzzy
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Homework Statement


The graph I have posted is the result of using a motion sensor above a bouncing ball.
I am asked to write a clear interpretation of the meaning of each parameter in the equation Y=At^2+Bt+C.

Homework Equations


Y=Ax^2+Bt+C
y=y0+v0t+1/2at^2

The Attempt at a Solution


http://imageshack.us/photo/my-images/687/screenshot20110902at112.png/
I think relating the above two equations that B is the initial velocity and C is the initial position. "A" however is confusing me.
Also if C is indeed the initial position I'm not quite sure I understand why it is negative.
 
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Megzzy said:

Homework Equations


Y=Ax^2+Bt+C
y=y0+v0t+1/2at^2

X in the first equation should be t. So how is A related to the parameter a ?

The ball moves under the effect of gravity - what is the value of a?

ehild
 
sorry didn't see that typo!

a would just be the gravitational acceleration correct? So -9.80 m/s^2?
I'm still confused as to how they relate though. Does that mean A is half that of the gravitational acceleration?
 
Megzzy said:
Does that mean A is half that of the gravitational acceleration?

Yes.

ehild
 
Alright thank you!
I'm just confused as to why it changes (shown on that graph)?
 
The parabola is upside-down, so the A parameter is negative (like the gravitational acceleration, which points downward) A=-9.8/2.

ehild
 

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