A law enforcement officer in an intergalactic “police car” turns on a red flashing light and sees it generate a flash every 3.5 s. A person on Earth measures that the time between flashes is 4.5 s. How fast is the “police car” moving relative to the earth?
just plug in your relativistic time dilation formula and solve for v.
To determine the speed of the "police car" relative to Earth, we can use the concept of time dilation from the theory of relativity. Time dilation states that the perceived time interval between two events will be different for two observers moving relative to each other.
In this case, we have the following information:
- The flashing light on the "police car" generates a flash every 3.5 seconds according to the officer.
- A person on Earth measures the time between flashes as 4.5 seconds.
Now, let's calculate the relative speed of the "police car" using the formula for time dilation:
v = c * (Δt_observed / Δt_reference - 1)
where:
v is the relative velocity,
c is the speed of light (approximately 299,792,458 meters per second),
Δt_observed is the time measured by the observer on Earth (4.5 seconds),
Δt_reference is the time measured by the officer in the "police car" (3.5 seconds).
Plugging in the values, we can calculate the relative velocity:
v = 299,792,458 * (4.5 / 3.5 - 1)
v = 299,792,458 * (1.2857 - 1)
v = 299,792,458 * 0.2857
v ≈ 85,714,285 meters per second
Therefore, the "police car" is moving relative to Earth at a speed of approximately 85,714,285 meters per second.