I am currently a 3rd year undergraduate electronic engineering student. I have completed a course in dynamics, calculus I, calculus II and calculus III. I have decided to self study a basic introduction to special relativity as it was not part of my physics syllabus and is not included in any of my other modules. The source I am using is the textbook "Fundamentals Of Physics(9th Edition)" by Halliday and Resnick.
I understand the concept of proper time and length, but I am interested in solving problems using the Lorentz transformations rather than using the length contraction and time dilation "short cuts."
For example, the following textbook sample problem:
I understand how the the answer was obtained, however I am wondering if it is possible to tackle the problem as follows; using just the Lorentz transformation equations and the equation of motion; x = vt and defining 2 events, i.e. [event 1] = point B passes Sally & [event 2] = point A passes Sally. I have tried this but I keep getting the wrong answer unless I use the length contraction formula. Is there a way to work out this problem in this manner based on the given information?
All answers on this will be greatly appreciated.