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A bomb is designed to explode 4.00 s after it is armed. The bomb is launched from Earth and accelerated to an unknown final speed. After reaching its final speed, however, observers on Earth see the bomb explode 6.5 s after it is armed. What is the final speed of the bomb just before it explodes?

A) 0.830c
B) 0.982c
C) 0.949c
D) 0.781c
E) 0.159c

Answer :

Final answer:

To calculate the final velocity of the bomb, we can use the time dilation equation from special relativity.

Explanation:

To solve this problem, we can use the time dilation equation from special relativity. The equation is given by:

t' = t / sqrt(1 - v^2/c^2)

where:

  • t' is the observed time interval
  • t is the proper time interval
  • v is the final velocity of the bomb
  • c is the speed of light

In this case, the proper time interval is 4.00 s, and the observed time interval is 6.5 s. Plugging these values into the equation, we can solve for the final velocity:

6.5 = 4.00 / sqrt(1 - v^2/c^2)

Simplifying the equation and solving for v, we find that the final velocity of the bomb is approximately 0.830c.

Learn more about time dilation here:

https://brainly.com/question/35889266

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Rewritten by : Brahmana