An observer moving at a speed of 0.820 c relative to a rod (Fig. P26.14) measure
ID: 2243235 • Letter: A
Question
An observer moving at a speed of 0.820 c relative to a rod (Fig. P26.14) measures its length to be 2.00 m and sees its length to be oriented at 30.0 o with respect to the direction of motion. What is the proper length of the rod?
What is the orientation angle in a reference frame moving with the rod?
An observer moving at a speed of 0.820 c relative to a rod (Fig. P26.14) measures its length to be 2.00 m and sees its length to be oriented at 30.0 o with respect to the direction of motion. What is the proper length of the rod? What is the orientation angle in a reference frame moving with the rod?Explanation / Answer
Here
Along the Directin of motion
Length = 2*Cos30
= 1.732 m
Actua length along x Direction = 1.732/sqrt(1 - 0.82^2)
= 3.026 m
Along vertical direction length remains same = 2*Sin(30)
= 1 m
So
Proper Length = sqrt(3.026^2 + 1^2)
= 3.187 m
angle = arctan(1/3.026)
= 18.287 degree