In the earth\'s reference frame, a tree is at the origin and a pole is at x =38k
ID: 1341738 • Letter: I
Question
In the earth's reference frame, a tree is at the origin and a pole is at x=38km. Lightning strikes both the tree and the pole at t=16s. The lightning strikes are observed by a rocket traveling in the x-direction at 0.7 c.
A)What are the spacetime coordinates xtree, xpole for these two events in the rocket's reference frame
B)What are the spacetime coordinates ttree, tpole for these two events in the rocket's reference frame?
C)
Are the events simultaneous in the rocket's frame? If not, which occurs first?
Are the events simultaneous in the rocket's frame? If not, which occurs first?
1. Yes, the events are simultaneous in the rocket's frame. 2. No, the lightning is observed to strike the pole before the tree. 3. No, the lightning is observed to strike the tree before the pole.Explanation / Answer
position of the tree : x1 = 0 Km
position of the pole = x2 = 38 km
Lightning strikes both the tree and the pole
at a time : t = 16 u s
speed of the Rocket = v = 0.7 c
lorentz factor : gamma = 1/sqrt(1-v^2/c^2)
gamma = 1/sqrt(1-0.7^2) = 1.4
space - coorinate : x' = gamma * (x1 - vt ) (for Tree)
x' = (1.4* 0.7* 3e8 * 16 e -6) = - 4.702 Km
space - cocorinates: x ' = gamma (x1 - vt )
x' = (1.4* 38 e 3 - 0.7 * 3e8 * 1.6 e-5 = 49.84 Km
Time co-ordinate ; t ' = gamma ( t - v x /c2) (for Tree)
t = 1.4 * 1.6 e -5 - 0.7* 3e8 *0/c2)
t = 2.24 e -5 or 22.4 us
Time co-ordinate : t ' = gamma ( t - v x /c2) (for pole)
t = (1.4*1.6 e -5 - 0.7* 3e 8 *38e 3 /9e16)
t = -88.66 us
C. 1 Yes, the events are simultaneous in the rocket's frame.