Solve Time Dilation: Get 24hr Solution in 105hrs

[EngageEngage]

[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.

 

[YellowTaxi]

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.

 

[EngageEngage]

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!