Q. 49 On a futuristic highway, a 15聽m... [FREE SOLUTION]

Chapter 36: Q. 49 (page 1061)

On a futuristic highway, a $15 m$ long rocket travels so fast that a red stoplight, with a wavelength of $700 n m$ , appears to the pilot to be a green light with a wavelength of $520 n m$ . What is the length of the rocket to an observer standing at the intersection as the rocket speeds through?

Short Answer

Expert verified

$L' = 1.449 脳 10^{- 2} k m 鈫� 14.49 m$ length of the rocket to an observer standing at the intersection as the rocket speeds through.

Step by step solution

Given Information

We need to find the length of the rocket to an observer standing at the intersection as the rocket speeds through.

Simplify

Consider,

$L = 15 m 鈫� 1.5 脳 10^{- 2} k m$

$位_{0} = 700 n m$

$位 = 520 n m$

First, finding $鈭� 位$ ,

$鈭� 位 = 位 - 位_{0} = 520 n m - 700 n m = - 180 n m$

Now finding velocity $v$ :

$\frac{鈭� 位}{位_{0}} = \frac{v}{c}$

$鈬� v = c \frac{鈭� 位}{位_{0}}$

$v = 3 脳 10^{5} k m / s (- \frac{180}{700})$

$v = - 7.714 脳 10^{4} k m / s$

Finally, we will find the length of the rocket $L'$

$L' = \sqrt[L]{1 - \frac{v^{2}}{c^{2}}} L' = 1.5 脳 10^{- 2} \sqrt{1 - \frac{{(- 7.714 脳 10^{2})}^{2}}{{(3 脳 10^{5})}^{2}}} L' = 1.449 脳 10^{- 2} k m 鈫� 14.49 m$

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91影视

On a futuristic highway, a $15 m$ long rocket travels so fast that a red stoplight, with a wavelength of $700 n m$ , appears to the pilot to be a green light with a wavelength of $520 n m$ . What is the length of the rocket to an observer standing at the intersection as the rocket speeds through?

Short Answer

Step by step solution

Given Information

Simplify

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91影视

On a futuristic highway, a 15mlong rocket travels so fast that a red stoplight, with a wavelength of 700nm, appears to the pilot to be a green light with a wavelength of 520nm. What is the length of the rocket to an observer standing at the intersection as the rocket speeds through?

Short Answer

Step by step solution

Given Information

Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Translational Dynamics

Electricity and Magnetism

Magnetism

Energy Physics

Fields in Physics

Atoms and Radioactivity

Study anywhere. Anytime. Across all devices.

On a futuristic highway, a $15 m$ long rocket travels so fast that a red stoplight, with a wavelength of $700 n m$ , appears to the pilot to be a green light with a wavelength of $520 n m$ . What is the length of the rocket to an observer standing at the intersection as the rocket speeds through?