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Problem 55 Hard Difficulty

An observer moving at a speed of 0.995 $c$ relative to a rod (Fig.P 26.55) measures its length to be 2.00 m and sees its length to be oriented at 30.0° with respect to its direction of motion. (a) What is the proper length of the rod? (b) What is the orientation angle in a reference frame moving with the rod?

Answer

a) 17.4 $\mathrm{m}$
b) $3.30^{\circ}$

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Video Transcript

well length along X is given by L X is equal to l times. Go sign feta. Well l is 2.0 Motive. My lie course final 30 degrees on this is equal to 1.7 32 meters. Also in lye. Well, l y equals l scientist and Eli's two points to close a door Multiply by signed turning degrees and this gives us one meter Well, lp along X is given by L X, divided by square root off one minus rescreened. Your mind it by C square. Well, we have a lex, which is 1.732 divided by our screen Rudolph one minus 0.9 mine five We'll square and simplifying this LP along axes 17.34 meters and also lb along. Why is it cool to know why? Which is equal to 1.0 meters? All right, well, l p is equal to square. Rudolph, um, I'll be along x whole square less ah LP along. Why whole scare now let's split into values. Still, L P is equal to square root off uh, 17.34 whole square less 1.0 whole scare. And this gives this 17.4 17.4 meters. Now let's find out angle Tito be is equal to, uh, Danny and worse into l'll be along. Why divided by Opie along X and this equals Danning. Worse. Hello, Payal. Unwise. 1.0 And that will be a long axes 17.34 and therefore feet A P is equal to three buying trains your degrees.

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