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Math Help - Escape velocity with scientific notation in a square root

  1. #1
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    Escape velocity with scientific notation in a square root

    Teachers instructions: Please enter answer using regular notation.

    Leaving Mars

    The spacecraft is designed to leave the surface of Mars with the first stage of its propulsion system and be put into Martian orbit. Then, the second stage is used to boost the spacecraft from Martian orbit into an interplanetary trajectory and return to Earth.
    If the spacecraft is in Martian orbit at an altitude of 341 km, what is the velocity (in km/s) required to escape the gravitational attraction of Mars. Note that the velocity direction and magnitude required to actually return to Earth may be different.


    My work so far:

    Mass of Mars (Mp): 6.392E23
    Radius of Mars (R): 3.395E6

    <---correct equation


    my answer came to 5.012761026 which is not right according to the electronic answering system in which the homework is completed on.

    also if you can show me how to solve it on a graphing calculator
    thanks for the help!!!!!
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  2. #2
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    you'll make calculations (and life) much easier for yourself if you use the "store" capability of the graphing calculator.

    to store a value ...

    1. type out the value
    2. hit the [STO] button
    3. hit the [ALPHA] button and select the letter you want to store the value into.
    4. press [ENTER] to store the value

    for example, to store the universal gravitational constant, your screen will display ...

    6.673E-11 -> G

    hit [ENTER] and it's done.

    store the mass of the planet in M ...

    6.392E23 -> M

    [ENTER]
    add the planet radius and the height and store in R ...
    (did you remember to change km to m for h?)

    3.395E6 + 3.41E5 -> R

    [ENTER]

    now all you have to do is type in and calculate ...

    \sqrt(2GM/R)

    you should get about 4778 m/s which you can change to km/s if that's the way you need to express it.
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  3. #3
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    what answer did you exactly get? i got 4778.488109 and that isnt working...
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  4. #4
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    nevermind i got it thank you!
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