Search: To find out answers to a specific question, copy a representative sentence from the question and paste the sentence in the search form and search it. The results show the most related questions and yours may be in there. Feel free to share LeiAcademy.org with other teachers and students.  
To discourage spam, only registered users can ask questions.

Welcome to Physics Homework and Study Help, where you can ask questions and receive help on learning physics. We currently focus on helping questions in introductory level college physics and high school AP Physics courses.
To discourage spam, only registered users can ask questions.

Facebook Twitter Google

Welcome to Physics Homework Help Page on LeiAcademy.org

Feel free to ask a question and also answer questions others asked. Answering others' questions can in turn help one's own understanding and build a warm healthy community for learning. The followings list a few things that might be helpful for you to effectively obtain help on specific physics homework or practice problems.  

Search: To find out answers to a specific questions, copy a representative sentence from the question and paste the whole sentence in the search form and search it. The results will show the most related questions and yours may be in there

Browse: To find out what have been discussed, asked or answered, put in a few key words in the search form and search for related questions, answers, and or solutions. Or you can click the related tags or other tabs to find useful information there. 

You can also write professional-looking equations using Latex codes (see details here).

This site is hosted on LeiAcademy.org, which will continue to add new resources for learning. Feel free to share this with other teachers and students.  

Spaceship Question

0 votes
95 views
On slide 20 of lecture L1402 could you explain each step towards getting the final solution of v=0.857c, I can't follow the calculations you made.

Thanks!!
asked Dec 10, 2013 in Intro College Physics by anonymous

1 Answer

0 votes

The observer on the earth sees the space ship passing by with velocity v. The earth observer also measures a different length of the spaceship than its proper length which is ||L=L_p/\gamma||. 

Now let's find the velocity v. The length of the spaceship measured by earth observer is L. It takes ||\Delta t=0.8\times 10^{-6}s|| to pass a point on the earth. Therefore, the speed is ||v=L/\Delta t||. So we have 
$$v=\frac {L}{\Delta t}=\frac {L_p/\gamma}{\Delta t}=\frac {400\sqrt{1-v^2/c^2}}{0.8\times 10^{-6}}$$

Now you can solve for v: first move the ||\sqrt{1-v^2/c^2}|| term to the left of the equation, so we have $$\frac{v}{\sqrt{1-v^2/c^2}}=\frac{400}{0.8\times 10^{-6}}=5\times 10^8$$

Square both sides and then divide both sides with c2, so we have $$\frac {v^2/c^2}{1-v^2/c^2}=\frac {25\times 10^{16}}{9\times 10^{16}}=\frac {25}{9}$$

Take ||v^2/c^2|| as one term, then you can solve it to have ||v^2/c^2=\frac{25}{34}||.

Therefore, ||v/c=\sqrt{25/34}=0.857|| and ||v=0.857c||. 

answered Dec 10, 2013 by PhysicsDude (21,750 points)
web counter
...