An event occurs in system K’ at x’ = 2 m, y’ = 3.5 m, z’= 3.5 m, and t’= 0. System K’ and K have their axes coincident at t = t’= 0, and system K’ travels along the x axis of system K with a speed 0.8c. What are the coordinates of the event in system K?
Answers
The coordinates of the event in system K can be found using the Lorentz transformation equations, and they are (10/3 m, 3.5 m, 3.5 m, 8/3 m/c).
The Lorentz transformation equations relate the coordinates of an event in one reference frame to the coordinates of the same event in another reference frame that is moving with a constant velocity relative to the first reference frame.
The equations are as follows:
x = γ(x' + vt')
y = y'
z = z'
t = γ(t' + vx'/c^2)
Where γ is the Lorentz factor, which is given by:
γ = 1/√(1-v^2/c^2)
In this case, v = 0.8c, so γ = 1/√(1-(0.8c)^2/c^2) = 5/3.
Plugging in the values for x', y', z', t', v, and γ into the Lorentz transformation equations, we get:
x = (5/3)(2 m + (0.8c)(0)) = 10/3 m
y = 3.5 m
z = 3.5 m
t = (5/3)(0 + (0.8c)(2 m)/c^2) = 8/3 m/c
Therefore, the coordinates of the event in system K are (10/3 m, 3.5 m, 3.5 m, 8/3 m/c).
To know more about Lorentz transformation equations, refer here:
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