According to observer o, two events occur separated by a time interval-at=0.48 us and at locations separated by 45 m (a) according to observer o, who is in motion relative to o at a speed of u=0.970c in the positive x direction, what is the time interval between the two events? 146 (b)what is the spatial separation between the two events, according to 07 349.1496

(a)

(b)

Explanation:

We use Lorentz transformations, since they relate the measures of a physical magnitude obtained by two different observers, these are:

Here is the spatial separation according to O, is the spatial separation according to O', is the time interval according to O,  is the time interval according to O', is the relative speed between the two observers and is the speed of light.  All we do now is write the quantities we were given, recall that

(a)

(b)

The minus sign means that the second event is closer for one observer and the first is closer for the other.

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