UFO - time taken to travel to moon

[ZedCar]

A UFO is observed just above the surface of the Earth moving at a constant velocity. An astronaut on the moon (3.8 x 10^8 m from earth) observes the UFO just above the surface of the moon 2.0s later.

From the UFO's reference frame, how long did it travel from the Earth to the moon?

The answer is given as 1.6s



I was using equation;

Δt = γΔt0

With t0 = 2 seconds

the velocity in γ I calculated to be 1.9x10^8 by using
v=distance/time
v=(3.8x10^8)/2
v=1.9x10^8

But I'm getting an incorrect answer of 2.58 seconds.

 

[Doc Al]

I was using equation;

Δt = γΔt0

With t0 = 2 seconds

You're mixing up Δt & Δt₀.

 

[ZedCar]

Thanks Doc Al.

Now I'm getting an answer of 1.547 seconds which is a lot better.

I'm not sure why the book has rounded the answer up to 1.6s

 

[Doc Al]

I'm not sure why the book has rounded the answer up to 1.6s

Beats me. I wouldn't worry about it.

The main thing is to know how and when to apply the time dilation formula.

 

[ZedCar]

Thank you