Final answer:
A person traveling at 120 km/h ages at 1/3 the rate of a person at rest. The length of a meter stick observed by the traveler is approximately 0.9684 m or 96.84 cm.
Step-by-step explanation:
(a) A person is traveling along an interstate highway at 120 km/h:
To determine the fraction of the rate at which a person traveling at 120 km/h ages compared to a person at rest, we need to calculate the person's velocity relative to the speed of light. Since the speed of light is 100 m/s in this hypothetical universe, the person's velocity can be calculated as:
120 km/h = 120,000 m/3,600 s = 33.33 m/s or 33.34 m/s.
The fraction of the rate at which the person ages compared to a person at rest is the ratio of their velocities:
Fraction = Velocity of traveler / Velocity of light = 33.33 m/s / 100 m/s = 0.3333 or 1/3
So, the person ages at 1/3 the rate of a person at rest.
(b) And This traveler passes by a meter stick at rest on the highway:
The length of the meter stick as observed by the traveler can be calculated using the relativistic length contraction formula:
Length = Length_0 / Gamma
Where Length_0 is the proper length of the meter stick at rest and Gamma is the Lorentz factor given by Gamma = 1 / sqrt(1 - (v^2 / c^2)), where v is the velocity of the traveler relative to the speed of light and c is the speed of light.
Since the length of the meter stick at rest is 1 meter, and the speed of light in this universe is 100 m/s, the Lorentz factor can be calculated as:
Gamma = 1 / sqrt(1 - (33.33^2 / 100^2))
Gamma ≈ 1.033
The length of the meter stick as observed by the traveler is given by:
Length = 1 m / 1.033 ≈ 0.9684 m or 96.84 cm.