69 The car-in-the-garage problem. Carman has just purchased the world's longest stretch limo, which has a proper length of 

. In Fig. 37-32a, it is shown parked in front of a garage with a proper length of 

. The garage has a front door (shown open) and a back door (shown closed). The limo is obviously longer than the garage. Still, Garageman, who owns the garage and knows something about relativistic length contraction, makes a bet with Carman that the limo can fit in the garage with both doors closed. Carman, who dropped his physics course before reaching special relativity, says such a thing, even in principle, is impossible.

 at the (now open) front door. Then Carman is to drive the limo directly toward the front door at a velocity of 

 (which is, of course, both technically and financially impossible). Carman is stationary in the 

 reference frame; Garageman is stationary in the 

There are two events to consider. Event 1: When the rear bumper clears the front door, the front door is closed. Let the time of this event be zero to both Carman and Garageman: 

 reference frame. Event 2 : When the front bumper reaches the back door, that door opens. Figure 37-32c shows event 2 according to the 

According to Garageman, (a) what is the length of the limo, (a) (b) (c)

37.P.69a

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37.P.69a

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