shortcake1970
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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calculusfunctions
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@shortcake1970 do you know the definition of a light year?
calculusfunctions
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A light year is the distance that light travels in one Earth year.
VeritasVosLiberabit
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light travels at 3*10^8 m/s
calculusfunctions
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Yes that's approximately the speed of light, as @VeritasVosLiberabit said.
VeritasVosLiberabit
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so it seems the 2*10^8 is meant to throw you off because it is irrelevant to finding the distance
shortcake1970
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and the distance light travels in a year is 9.47 X 10^15 i have that much
calculusfunctions
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Now find the number of seconds in one Earth year. Yes @VeritasVosLiberabit , that is extraneous information. Not needed.
VeritasVosLiberabit
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it might be better to keep your calculations in MKS units unless told otherwise.
calculusfunctions
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Alright @shortcake1970 now simply multiply that answer by 50.
shortcake1970
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so do I just multiply?
calculusfunctions
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Haha that's what I said.
shortcake1970
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oops yup you just answered that
shortcake1970
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Thank you!
calculusfunctions
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Need help with anything else or are you okay?
shortcake1970
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well I do have another questions I might need help with let me write it...
calculusfunctions
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Are these questions you've tried yourself? It's important you try them yourself first.
shortcake1970
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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
shortcake1970
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once i know which formula i can work it out myself :)
calculusfunctions
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Sorry I was away for a minute. Just give me second. I'm just in the middle of something.
shortcake1970
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ok i'm having a hard time typing the formula
shortcake1970
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delta t=delta t o /square root of 1-v^2/c^2
calculusfunctions
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OK I'm back. Yes\[\Delta t =\frac{ \Delta t _{0} }{ \sqrt{1-\frac{ v ^{2} }{ c ^{2} }} }\]
calculusfunctions
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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\[\Delta t _{0}=\Delta t \sqrt{1-\frac{ v ^{2} }{ c ^{2} }}\]
shortcake1970
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.90 x 10^8 s
calculusfunctions
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Give me a second to calculate it.
shortcake1970
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is the answer for the previous question 4.73 x 10^17?
calculusfunctions
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It should be\[9.0\times10^{-9}\]
calculusfunctions
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That exponent is negative 9
shortcake1970
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oh i see
calculusfunctions
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Do you? Did you spot your error?
shortcake1970
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yes i spotted the error
calculusfunctions
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Great. I have to go but is there anything else before I do?
calculusfunctions
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I guess not. I might be back a little later. Bye.
shortcake1970
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thank you so much.