An alley is 1000 m long. A small explosion goes off at the north end end and 15

Question

An alley is 1000 m long. A small explosion goes off at the north end end and 15 seconds later another one occurs at the south end. All these measurements are given with respect to an observer in the alley reference frame. A car moving at 0.6 c moves from south to north. Draw event diagrams for the frame of the alley and the frame of the car. What is the magnitude of the spatial separation, that is, the distance between the location at which one explosion occurs and the location at which the other explosion occurs a) in the frame of the alley, and b) in the frame of the car.

I know for the frame of the alley the answer is 1000m and I understand that. I also know that the answer for part b is 3.4x10^9m but I do not understand how that answer is reached. I keep getting 800m

Explanation / Answer

the time difference between two events is

t=to/sqrt[1-(v/c)2]=15/sqrt(1-0.62)

t=18.75 sec

The distance between two events in the frame of the car

d=(0.6*3*108)*18.75

d=3.375*109 m =3.4*109 m (approx)

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