- #1
TristanRE
- 6
- 0
Homework Statement
"Two people stand a distance L apart along an east–west road. They both clap their hands at
precisely noon in the ground frame. You are driving eastward down this road at speed 4c/5. You
notice that you are next to the western person (W) at the same instant (as measured in your frame)
that the eastern person (E) claps. Later on, you notice that you are next to a tree at the same
instant (as measured in your frame) that the western person claps. Where is the tree along the
road? (Describe its location in the ground frame by computing how far to the east of W it is.)"
Homework Equations
"rear clock ahead": t = Lv/c^2
gamma = 1/sqrt(1-v^2/c^2)
d=vt
t_A = gamma*t_B
The Attempt at a Solution
So I have obtained 2 answers, and I'm unsure which is correct.
By looking at it from my frame, and noting that "Rear clock ahead" tells me that E will clap t = Lv/c^2 =4L/5c before W, I know that (in my frame) the tree will travel towards me at v = 4c/5, and will travel for time t. Therefore: d = v*t = 4c/5*4L/5c=16L/25.
I'm confused though, for the questions asks me to give the distance from the ground frame. Is the above correct? I believe that its not, and that I have to adjust the distance obtained by the gamma factor (3/5) because of length contraction.
Therefore L(ground) = L(for me)/gamma = 16L/25*5/3 = 16L/15.
What gives me confidence in this is that I get the same answer if I instead adjust the time it takes the tree to move (in the ground frame, the time that I move for) using the equality t(ground) = gamma*t(me) (for the ground frame).
I'm having a hard time justifying either of these in my head. Which is correct?
Thanks for the help.