Fairly simple (I assume) acceleration derivation I've blanked on

[Jonnoley]

Hi, I understand this is probably not at all complicated, but I've completely blanked and I've been working at it for hours now.

Homework Statement

Derive the expression g=2(L₂t₁-L₁t₂)/t₁t₂(t₁+t₂)

I've replaced the lower case ls there with upper case one's for clarity, but it's just two distances, L₁ and L₂

This relates to a simple experiment to measure g I'm currently doing a lab report for, where L₁ and L₂ are the distances between some infrared sensors on the drop tower, and t₁ t₂ are the times for the ball I dropped to pass between the sensors.

Homework Equations

I have no idea, I've tried every equation of motion and every mathematical operation I could.

The Attempt at a Solution

I have tried substituting Δt, ΔL and Δv into L=vt+(at²)/2 and have got some fairly close answers, but have also proved acceleration doesn't exist several times, so that might be barking up the wrong tree, in the wrong forest, on the wrong planet.

 

[Steely Dan]

This should be in the lower level physics forum, but no matter. Another relevant equation that you might want to try using is $$v_f^2 = v_0^2 - 2 g d.$$ That should help you eliminate some of the velocities (that you don't ultimately care about) from the other kinematics equation you listed.