# Measuring acceleration of gravity

1. Nov 26, 2007

### tronter

[SOLVED] Measuring acceleration of gravity

1. The problem statement, all variables and given/known data

The acceleration of gravity can be measured by projecting a body upward and measuring the time that it takes to pass two given points in both directions.

Show that if the time the body takes to pass the horizontal line $$A$$ in both directions is $$T_A$$, and the time to go by a second line $$B$$ in both directions $$T_B$$, then, assuming that the acceleration is constant, its magnitude is $$g = \frac{8h}{T_{A}^{2} - T_{B}^{2}}$$ where $$h$$ is the height of line $$B$$ above line $$A$$.

2. Relevant equations

3. The attempt at a solution

I am not sure how to approach this. I know that $$g = 9.8$$. The path the body takes is a parabola. And $$a = \dot{v}$$.

Last edited: Nov 26, 2007
2. Nov 26, 2007

### tronter

Since the path is a parabola, I would expect there to be a quadratic term?

3. Nov 27, 2007

### robphy

Draw a y-vs-t graph of the motion.... a parabola.
Mark the two heights with $$y_B> y_A$$.
Note that there are four events.. label them sequentially as "1" (at A), "2" (at B), "3" (at B), "4" (at A).
Do you know any relationships among any of the quantities at those events?

Last edited: Nov 27, 2007
4. Nov 27, 2007

### robphy

By the way, this sounds like a Kleppner-Kolenkow problem.

5. Nov 27, 2007

### tronter

yes it is. I already solved it.

Thanks

6. Nov 27, 2007

### robphy

Great!
Did my hint help? Or did you come up with it yourself?
Or did you use a different approach?

7. Nov 27, 2007

### tronter

Yeah I just used $$y = y_0 + v_{y0}t - \frac{1}{2}gt^{2}$$ where we consider $$y_0 = y_A$$ and $$y_0 = y_B$$.

Then solve a quadratic, subtract, and rearrange.

8. Nov 27, 2007

### robphy

I see. Good.
My method avoids solving a quadratic explicitly by using
the velocity and velocity-squared kinematic equations and some symmetry.

9. May 29, 2011

### John O' Meara

Re: [SOLVED] Measuring acceleration of gravity

I have it now as I found the same problem in classical physics Thanks anyway