Fireworks go off at the same time according to Earth clocks in two cities,Alum and Boron,that are 300 km apart.The people in a spaceship that is flying in a straight line from Alum to Boron at 0.80 c also observe the fireworks.Do they see the fireworks in the two cities simultaneously? If the people in the spaceship say the fireworks were not simultaneous in Alum and Boron,how long before or after the fireworks flashed at Alum did the fireworks flash at Boron according to their calculations? (The spaceship is directly over Alum when the fireworks flash. ) A)Yes;0 B)Before;1.0 *10 ^- ³ s C)After;1.0 *10 ^- ³ s D)Before;1.3 *10 ^- ³ s E)After;1.3 *10 ^- ³ s

Question

Quizplus · Accepted Answer

From the perspective of the people in the spaceship, the distance between Alum and Boron is contracted due to length contraction. The contracted distance can be calculated as follows:

L' = L / γ

where L is the proper distance between Alum and Boron (300 km) and γ is the Lorentz factor for the velocity of the spaceship (0.8 c).

γ = 1 / sqrt(1 - v^2/c^2)
   = 1 / sqrt(1 - 0.8^2)
   = 1.67

L' = 300 km / 1.67
   = 180 km

Since the spaceship is directly over Alum when the fireworks are observed, the observed time difference between the fireworks in Alum and Boron can be calculated using the following formula:

Δt' = Δx' / v

where Δx' is the contracted distance between Alum and Boron (180 km) and v is the velocity of the spaceship (0.8 c).

Δt' = 180 km / (0.8 c)
     = 562.5 s
     ≈ 9.4 min

This means that according to the people in the spaceship, the fireworks in Boron will be observed about 9.4 minutes after the fireworks in Alum. Therefore, the best answer is D: Before; 1.3 s.

Fireworks Go Off at the Same Time According to Earth