## shortcake1970 2 years ago if you were to travel to a star 50 light years from earth at a speed of 2.0 X 10 to 8th power m/s, what would you measure this distance to be?

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1. calculusfunctions

@shortcake1970 do you know the definition of a light year?

2. calculusfunctions

A light year is the distance that light travels in one Earth year.

3. VeritasVosLiberabit

light travels at 3*10^8 m/s

4. calculusfunctions

Yes that's approximately the speed of light, as @VeritasVosLiberabit said.

5. VeritasVosLiberabit

so it seems the 2*10^8 is meant to throw you off because it is irrelevant to finding the distance

6. shortcake1970

and the distance light travels in a year is 9.47 X 10^15 i have that much

7. calculusfunctions

Now find the number of seconds in one Earth year. Yes @VeritasVosLiberabit , that is extraneous information. Not needed.

8. VeritasVosLiberabit

it might be better to keep your calculations in MKS units unless told otherwise.

9. calculusfunctions

Alright @shortcake1970 now simply multiply that answer by 50.

10. shortcake1970

so do I just multiply?

11. calculusfunctions

Haha that's what I said.

12. shortcake1970

oops yup you just answered that

13. shortcake1970

Thank you!

14. calculusfunctions

Welcome!

15. calculusfunctions

Need help with anything else or are you okay?

16. shortcake1970

well I do have another questions I might need help with let me write it...

17. calculusfunctions

Sure

18. calculusfunctions

Are these questions you've tried yourself? It's important you try them yourself first.

19. shortcake1970

a beam of a certain type of elementary particle travels at a speed of 2.8 X 10^8 m/s. at this speed the average lifetime is measured to be 2.5 X 10^-8 s. what is the particle's lifetime at rest. let me tell you what formula i was thinking of using

20. shortcake1970

once i know which formula i can work it out myself :)

21. calculusfunctions

Sorry I was away for a minute. Just give me second. I'm just in the middle of something.

22. shortcake1970

ok i'm having a hard time typing the formula

23. shortcake1970

delta t=delta t o /square root of 1-v^2/c^2

24. calculusfunctions

OK I'm back. Yes$\Delta t =\frac{ \Delta t _{0} }{ \sqrt{1-\frac{ v ^{2} }{ c ^{2} }} }$

25. calculusfunctions

Do you understand? $\Delta t = 2.5\times10^{-8}s$$v =2.8\times10^{8}m/s$$c =3.0\times10^{8}m/s$$\Delta t _{0}=?$Rearrange the formula first to get$\Delta t _{0}=\Delta t \sqrt{1-\frac{ v ^{2} }{ c ^{2} }}$

26. shortcake1970

.90 x 10^8 s

27. calculusfunctions

Give me a second to calculate it.

28. shortcake1970

is the answer for the previous question 4.73 x 10^17?

29. calculusfunctions

It should be$9.0\times10^{-9}$

30. calculusfunctions

That exponent is negative 9

31. shortcake1970

oh i see

32. calculusfunctions

Do you? Did you spot your error?

33. shortcake1970

yes i spotted the error

34. calculusfunctions

Great. I have to go but is there anything else before I do?

35. calculusfunctions

I guess not. I might be back a little later. Bye.

36. shortcake1970

thank you so much.