1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Physics question involving trig.

  1. Oct 29, 2013 #1
    An astronaut arrives on the planet Oceania and climbs to the top of a cliff overlooking the sea. The astronaut’s eye is 100 m above the sea level and he observes that the horizon in all directions appears to be at angle of 5 mrad below the local horizontal.

    What is the radius of the planet Oceania at sea level?

    How far away is the horizon from the astronaut?

    [Hint: the line of sight from the astronaut to the horizon is tangential to surface of the planet at sea level.]


    Having drawn out the problem I have two equations:
    Pythagoras: x^2 + R^2 = (R+100)^2
    Sine Law: x= (R+100)sinA

    x is the distance between the horizon and the astronaut
    R is the radius of the planet
    A is the angle between the two lengths of radius of the planet (sorry might sound a bit confusing, it makes more sense if you draw it out!)

    I then tried to combine them and solve for the radius of the planet R but im not having any luck getting the right answer :(

    Any steps, answer, and/or hints are all greatly appreciated! :)
     
  2. jcsd
  3. Oct 29, 2013 #2

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Welcome to PF;

    It helps to be careful about what you call things...

    You should have drawn a triangle OAB.
    O is at the center of the planet.
    A is where the astronaut is standing,
    B is on the surface of Oceania at sea level.

    Angles:
    The angle OBA is ##\frac{\pi}{2}## (working in radians).
    The angle AOB is ##\alpha##
    The angle OAB is ##\frac{\pi}{2}-\alpha##

    Lengths of the sides:
    ##|OB|=R## (radius of Oceania at sea level)
    ##|OA|=R+a## (a=100m) it is best to keep variables.
    ##|AB|=x = R\tan\alpha##

    You will also need another triangle: ABC
    points A and B are as before.
    point C is on the same line as OB, further out from Oceania.
    The line AC is perpendicular to the line OA.
    The angle CAB is given to you - from the drawing you should be able to see how it is related to ##\alpha##.

    You now have three right-angled triangles.
    ... but I'm afraid you'll probably have to attach a diagram.
     
  4. Oct 29, 2013 #3
    Thank you, I followed the steps you have given me and I drew the first triangle, however im having trouble understanding where the line AC should go, I made the AC line red in the diagram, im not sure if I drew it correctly. I attached the diagram which I drew in a word doc., I don't know any other way of drawing diagrams online, I hope its not an inconvenience.
     

    Attached Files:

  5. Oct 29, 2013 #4

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    The line AC is supposed to be the local horizontal to A (the Astronaut).
    The line AB is the line to the horizon as seen from A.


    It is poor netiquette to post attachments in poorly documented formats like docx - or any MS Office format.
    Not everyone can read them.

    For diagrams, please use png or gif format.
    For photographs: jpg is usually good enough.
    For general documents, please use an open document format or pdf

    The attachment function of PF lets you upload from your computer - another approach is to use a service like google-docs.
     
    Last edited: Oct 29, 2013
  6. Oct 29, 2013 #5
    From your figure, R/(R+a) = cosα. You know α, so you can calculate R.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted