Calculating Acceleration of Gravity w/ Kinematics

[jesuslovesu]

Homework Statement

The acceleration of gravity can be measured by project 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 a horizontal line A in both directions is Ta and the time to go by a second line B in both directions is Tb then assuming that the acceleration is constant, its magnitude is g = 8h/(Ta^2-Tb^2)

Homework Equations

y = y0 + 1/2 g t^2 + vot

The Attempt at a Solution

There is a diagram where A is the lower position and B is the higher position, they are separated by a distance h.

I found Ta = -2/g vy and Tb = -vy +- sqrt(vy^2 - 2gh)
but I really don't know where to go after this...
If I want acceleration a = dv/dt and v = dx/dt but I'm not quite sure what to do next... If I say delta T = Ta - Tb but that's all i can get.

 

[mezarashi]

You'll need 2 equations to solve this problem:

1. Express the initial velocities Va and Vb as a function f(g,ta) and f(g,tb) respectively. This can be done using the s = vt + 0.5at^2 kinematics equation.

2. Use the kinematics equation: Vb^2 = Va^2 + 2gh

From equation 2, you can substitute out Vb and Va into a function purely of g and t. From there, it's just algebra. Good luck.