Chapter 36: Q. 16 (page 1059)

a. At what speed, as a fraction of $c,$ must a rocket travel on a journey to and from a distant star so that the astronauts age $10$ years while the Mission Control workers on earth age $120$ years?
b. As measured by Mission Control, how far away is the distant star?

Short Answer

Expert verified

$a .) v = 0.9965 c b .) ∆ x = 119.58 l y$

Step by step solution

Part (a) Step 1: Given Information

We have given that,

∆ τ = 10 years ∆ t = 120 years

Part (a) Step 2: Simplify

We have to find speed $v,$ as a fraction of $c,$ must a rocket move on a journey.

$∆ t = \frac{∆ τ}{\sqrt{1 - β^{2}}} ∆ t = \frac{1}{\sqrt{1 - β^{2}}} \frac{120}{10} = \frac{1}{\sqrt{1 - {(\frac{v}{c})}^{2}}} (Substitutevaluesinequation.) 12 = \frac{1}{\sqrt{1 - {(\frac{v}{c})}^{2}}}$

$1 - {(\frac{v}{c})}^{2} = {(\frac{1}{12})}^{2} {(\frac{v}{c})}^{2} = 1 - {(\frac{1}{12})}^{2} \frac{v}{c} = \sqrt{1 - {(\frac{1}{12})}^{2}} v = \sqrt{1 - {(\frac{1}{12})}^{2} c} v = 0.9965 c$

Part (b) Step 1: Given Information

We have given that,

∆ τ = 10 years ∆ t = 120 years

Part (b) Step 2: Simplify

We need to figure out how far away the distant star is.

$∆ x = v ∆ t ∆ x = 0.9965 c \times (120 y) (Substitutevaluesinequation.) ∆ x = 0.9965 \frac{l y}{y} \times (120 y) ∆ x = 119.58 l y$

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a. At what speed, as a fraction of $c,$ must a rocket travel on a journey to and from a distant star so that the astronauts age $10$ years while the Mission Control workers on earth age $120$ years?
b. As measured by Mission Control, how far away is the distant star?

Short Answer

Step by step solution

Part (a) Step 1: Given Information

Part (a) Step 2: Simplify

Part (b) Step 1: Given Information

Part (b) Step 2: Simplify

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a. At what speed, as a fraction of c,must a rocket travel on a journey to and from a distant star so that the astronauts age 10years while the Mission Control workers on earth age 120years?b. As measured by Mission Control, how far away is the distant star?

Short Answer

Step by step solution

Part (a) Step 1: Given Information

Part (a) Step 2: Simplify

Part (b) Step 1: Given Information

Part (b) Step 2: Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Magnetism

Thermodynamics

Quantum Physics

Nuclear Physics

Fields in Physics

Turning Points in Physics

Study anywhere. Anytime. Across all devices.

a. At what speed, as a fraction of $c,$ must a rocket travel on a journey to and from a distant star so that the astronauts age $10$ years while the Mission Control workers on earth age $120$ years?
b. As measured by Mission Control, how far away is the distant star?