Question

1. Suppose the straight-line distance between New York and San Francisco is 4.1 × 10⁶ m (neglecting the curvature of the earth). A UFO is flying between these two cities at a speed of 0.59crelative to the earth. What do the voyagers aboard the UFO measure for this distance?

2. A particle known as a pion lives for a short time before breaking apart into other particles. Suppose a pion is moving at a speed of 0.987c, and an observer who is stationary in a laboratory measures the pion's lifetime to be 2.7 × 10^-8 s. (a) What is the lifetime according to a hypothetical person who is riding along with the pion? (b) According to this hypothetical person, how far does the laboratory move before the pion breaks apart?

Answer 1

2Ans:

given data are speed (v) = 0.987c,

time(t) = 2.7*10^-8 sec   

By using time dialation formula

where t = time in the observer's frame and

t' = time in the moving system's frame

We know and

Therefore the lifetime according to a hypothetical person who is riding along with the pion is t= 4.33*10^-9s

Now the laboratory appears to move toward the pion at v = 0.996 c. So it covers a distance x:

  

Therefore the laboratory moves 1.28m before the pion breaks apart