# A spacecraft with a proper length of 300 m passes by an observer on the Earth. According to this observer, it takes 0.750 μ s for the spacecraft to pass a fixed point. Determine the speed of the spacecraft as measured by the Earth-based observer.

### Physics for Scientists and Enginee...

9th Edition
Raymond A. Serway + 1 other
Publisher: Cengage Learning
ISBN: 9781305116399

Chapter
Section

### Physics for Scientists and Enginee...

9th Edition
Raymond A. Serway + 1 other
Publisher: Cengage Learning
ISBN: 9781305116399
Chapter 39, Problem 39.19P
Textbook Problem
638 views

## A spacecraft with a proper length of 300 m passes by an observer on the Earth. According to this observer, it takes 0.750 μs for the spacecraft to pass a fixed point. Determine the speed of the spacecraft as measured by the Earth-based observer.

To determine
The speed of the spacecraft as seen by an earth based observer.

### Explanation of Solution

Given info: The proper length of the spacecraft is 300m and the time taken by the spacecraft to pass a fixed point is 0.750μs

The formula to calculate the relative length of the spacecraft is,

LLp=1(vc)2L=Lp1(vc)2

Here,

L is the length of the spacecraft as seen by the observer.

Lp is the actual length of the spacecraft.

v is the speed of the spacecraft.

c is the speed of the light.

The formula to calculate the speed of the spacecraft is,

v=LΔtΔt=Lv

Here,

Δt is the difference of time between the light approaching.

Substitute Lp1(vc)2 for L in above equation to form the relation.

Δt=Lp1(vc)2vΔt=Lp1v21c21v2=1c2+(ΔtLp)2

Substitute 3×108m/s for c , 300m for Lp and 0

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