The spaceship Lilac, based on the Purple Planet, is 721 m long when measured at rest. When the Lilac passes Earth, observers there measure i

Question

The spaceship Lilac, based on the Purple Planet, is 721 m long when measured at rest. When the Lilac passes Earth, observers there measure its length to be 661 m. At what speed v is the Lilac moving with respect to Earth? Express your answer as a multiple of the speed of light c.

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Kim Cúc 3 years 2021-09-05T08:13:40+00:00 1 Answers 14 views 0

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  1. huyenthanh
    0
    2021-09-05T08:15:24+00:00
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    Answer:

    The speed of Lilac is 0.399c.

    Explanation:

    The size of spaceship Lilac measured at the rest position = 721 m  

    The length of  Lilac when it passes Earth = 661 m

    Below is the calculation for speed at which Lilac is moving.

    Here, L, is the length of spaceship when it passes the earth.

    L_{0} is the length of spaceship measured at rest.

    V is the speed.

    L = L_{0}\sqrt{1-\frac{v^{2}}{c^{2}}} \\

    1-\frac{v^{2}}{c^{2}} = \left ( \frac{L}{L_{0}} \right )^{2} \\

    \frac{v}{c} = \sqrt{1-\left ( \frac{L}{L_{0}} \right )^{2}} \\

    \frac{v}{c} = \sqrt{1-\left ( \frac{661}{721} \right )^{2}} \\

    v = 0.399c

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