Problem 1-2
Problem 1-2:
You are walking at 2 m/s down a straight road, which is aligned wiht the x-axis. At time t=0s you sneeze. at time t=5s a dog barks, and at the moment he barks he is x=10m ahead of you in the road. At time t=10s a car which is just then 15m behind you backfires.
a.) Plot the positions x and times t of the sneeze, bark and backfire, relative to you, on a 2D graph. Label the points.
b.) Plot positions x' and times t' of the sneeze, bark and backfire, relative to an observer standing still, at the position at which you sneezed. Assume your watches are synchronized.
Solution:
Frames of reference:
Me (S)
Dog-Car-Other Observer (S')
The velocities in the problem are:
vSS'=2 m/s
Coordinates (xi,ti) are given in units of (m,s}.
Event 1: I sneeze. (x1,t1)=(0,0)
Event 2: Dog barks. (x2,t2)=(10,5)
Event 3: Car backfires. (x3,t3)=(-15,10)
a.) Since we can't plot graphs here, we will have to be satisfied with writing down the ordered pairs. For part a.), they happen to be just as I wrote them down above.
b.) This is asking us to look at the same 3 events, but from the point of view of S'. For this we can use the Galilean transformation:
xi'=xi+vSS't
to get:
(x1',t1')=(0,0)
(x2',t2')=(20,5)
(x3',t3')=(5,5)
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edit: typo
