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23 June, 15:34

Braving blizzard conditions on the planet Hoth, Luke Skywalker sets out at top speed in his snowspeeder for a rebel base 4800 mi away. He travels into a steady head wind and makes the trip in 3 hr. Returning, he finds that the trip back, still at top speed but now with a tailwind, takes only 2 hr. Find the top speed of Luke's snow speeder and the speed of the wind.

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  1. 23 June, 16:24
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    v_top = 2400 mi/hr

    v_w = 400 mi/h

    Step-by-step explanation:

    Given:

    - Total distance D = 4800 mi

    - Headwind journey time taken t_up = 3 hr

    - Tailwind journey time taken t_down = 2 hr

    Find:

    Find the top speed of Luke's snow speeder and the speed of the wind.

    Solution:

    - The speed of Luke v_l is in stationary frame is given by:

    v_l = v_w + v_l/w

    Where,

    v_w: Wind speed

    v_l/w: Luke speed relative to wind.

    - The top speed is attained on his returned journey with tail wind. We will use distance time relationship to calculate as follows:

    v_top = D / t_down

    v_top = 4800 / 2

    v_top = v_down = 2400 mi/hr

    - Similarly his speed on his journey up with head wind was v_up:

    v_up = D / t_up

    v_up = 4800 / 3

    v_up = 1600 mi/hr

    - Now use the frame relations to find the wind speed v_w:

    v_down = v_w + v_l/w

    v_up = - v_w + v_l/w

    - Solve equations simultaneously:

    2400 = v_w + v_l/w

    1600 = - v_w + v_l/w

    4000 = 2*v_l/w

    v_l/w = 2000 mi/h

    v_w = 400 mi/h
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