Two firecrackers explode at the same place in
a rest frame with a time separation of 11 s in
that frame.
Find the time between explosions according
to classical physics, as measured in a framemoving with a speed 0.7 c with respect to the
rest frame.
Answer in units of s
To find the time between the explosions according to classical physics as measured in a frame moving with a speed of 0.7 c (speed relative to the rest frame), we can make use of the concept of time dilation.
Time dilation is a phenomenon in special relativity where the time measured in one frame of reference appears stretched or dilated when observed from another moving frame. The formula for time dilation is given by:
Δt' = γ * Δt
Where Δt' is the time interval observed in the moving frame, Δt is the time interval in the rest frame, and γ (gamma) is the Lorentz factor, which is calculated as:
γ = 1 / √(1 - (v^2 / c^2))
In this case, we are given the time separation of 11 s in the rest frame. So, Δt = 11 s.
Now, we need to determine the Lorentz factor using the velocity relative to the rest frame. Given that the velocity is 0.7 c, we can substitute this value into the formula for γ:
γ = 1 / √(1 - (0.7^2 / 1^2))
Simplifying this equation will give us the value of γ.
Once we have the Lorentz factor, we can calculate the time interval observed in the moving frame using the formula:
Δt' = γ * Δt
Substituting the values we have, we can find the time between explosions in the moving frame, which will be the final answer in units of seconds.