# Solve Time Dilation: Get 24hr Solution in 105hrs

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In summary, the question is about a bomb placed on a space probe that is set to explode after 24 hours. The probe travels away from Earth at a speed of 0.9c and the observers on Earth are wondering how long it will take for them to see the flash of light from the explosion. The solution involves using the equation \Delta\tau=\Delta t \sqrt{1-\frac{v^{2}}{c^{2}}}, where \Delta\tau represents the proper time and \Delta t represents the time observed on Earth. After some calculations, it is determined that the total time for the observers on Earth to see the explosion is 104.5 hours, including the time for the light to travel back
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[SOLVED] Time Dialation Help

## Homework Statement

A bomb is placed on a space probe just before it's launched. The timer is set to trigger the bomb after exactly 24hrs. The probe travels away from Earth on a straight line at v=.9c. How long after launch will the observers on the Earth see the flash of light from the exploding bomb?

## Homework Equations

$$\Delta\tau=\Delta t \sqrt{1-\frac{v^{2}}{c^{2}}}$$

## The Attempt at a Solution

$$\Delta\tau = 24hrs.$$

$$\Delta t = \frac{24hrs}{\sqrt{1-.9^{2}}} = 55hrs$$
But, the textbook gives a time of 105hrs. Can anyone please tell me why what I did is wrong? This seems like a straightforward problem and I have no clue where I mesed up. Any help is greatly appreciated.

You're half way,
I think you need to add time for the light from the explosion to get back to Earth - which is when people on Earth see the explosion
Calc how far away it is.
Then calc the time for light to travel that distance.

Then,
$$\Delta x = .9c(55hrs)$$
$$t = \frac{.9c(55hrs)}{c} = 49.5 hrs$$
$$55+49.5=104.5$$

Thank you for the help, I completely blanked that part!

## What is time dilation?

Time dilation is a phenomenon in which time appears to move slower for an object or person who is moving at high speeds relative to another object or person.

## How does time dilation occur?

Time dilation occurs due to the principles of special relativity, which state that time and space are relative to the observer's frame of reference. When an object moves at high speeds, its perception of time is different from that of a stationary observer.

## How does one solve time dilation?

To solve time dilation, you need to use the formula t' = t * √(1 - v^2/c^2), where t' is the perceived time, t is the actual time, v is the velocity, and c is the speed of light. This formula allows you to calculate the difference in time between two frames of reference.

## Why does it take 105 hours to get a 24-hour solution for time dilation?

The 105-hour time frame is based on a scenario known as the "twin paradox," in which one twin travels at high speeds while the other twin remains stationary. The traveling twin experiences time dilation, causing them to age slower. When they return to their stationary twin after 105 hours, they will have experienced only 24 hours, resulting in a 24-hour solution for time dilation.

## What are some practical applications of time dilation?

Time dilation has significant implications in fields such as space travel, GPS systems, and particle accelerators. It is also a crucial concept in understanding the universe's fundamental principles, including the speed of light and the nature of time and space.

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