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Man in mirror

  1. Mar 25, 2009 #1
    1. The problem statement, all variables and given/known data
    --------------------------------------------------------------------------------

    You are preparing to go shopping for a plane mirror that will be hung on the wall of your dressing room. Your overall height is H = 2.3 m, and the vertical distance from the floor to the mid-line of your eyes is H1 = 2.18 m. You want the mirror to be tall enough to allow you to view your entire body from the tip of your head to the soles of your feet, while standing a horizontal distance D = 2.7 m from the mirror. Being frugal, you want to purchase the smallest possible mirror.

    (a) What height d above the floor should the bottom of the mirror be mounted?

    d = 1.09m
    (b) What is the minimum required mirror height (vertical dimension)?

    hmin = 1.15m
    (c) If instead, you want to be able to view your entire body in the mirror while standing at twice the distance away, D' = 6 m, what is the minimum required mirror height in this case?

    h'min = 1.15m
    (d) Return now to the mirror height and viewing distance of part (b). Suppose you wish to take a picture of yourself in the mirror using a camera that you hold exactly at mid-height (lens at a distance H/2 above the floor). What height s above the floor should you place the top of the mirror so that the top of your head is just included in the image? (Assume the camera field-of-view is wide enough to image the entire mirror.)

    s = ????? m


    (e) In the configuration of part (d), what amount ΔH of your lower body (feet and legs) will be cut off in the photographic image?

    ΔH = 0m
    (f) If you move toward the mirror at 3.6 m/s, how fast will your image be moving toward you?

    |v| = 7.2 m/s



    2. Relevant equations

    mirror = 1/2 h to see full height of man

    3. The attempt at a solution

    I cannot seem to get a right answer for part d no matter what I do.
    Camera is at 1.15m off the ground and has to be at least 1.15m tall
     
  2. jcsd
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