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

$L' = 1.449 \times 10^{- 2} k m \to 14.49 m$ 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,

$L = 15 m \to 1.5 \times 10^{- 2} k m$

$λ_{0} = 700 n m$

$λ = 520 n m$

First, finding $∆ λ$ ,

$∆ λ = λ - λ_{0} = 520 n m - 700 n m = - 180 n m$

Now finding velocity $v$ :

$\frac{∆ λ}{λ_{0}} = \frac{v}{c}$

$\Rightarrow v = c \frac{∆ λ}{λ_{0}}$

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

$v = - 7.714 \times 10^{4} k m / s$

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

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

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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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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

Fluids

Electric Charge Field and Potential

Wave Optics

Radiation

Fundamentals of Physics

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?