Determine the scale of the aerial photograph where: f=80mm, H=5500m and h=3560m. please round the answer to the nearest thousand

Geospatial Science

ScanSolve AI Answer

Answer

1:24000

Step-by-step solution

4 steps

The scale of an aerial photograph is determined by the ratio of the focal length of the camera to the flying height above the ground.

  1. Convert focal length to meters

    The focal length ff is given in millimeters, so convert it to meters to match the units of height.
    f=80 mm=80×10−3 m=0.080 mf = 80\ \text{mm} = 80 \times 10^{-3}\ \text{m} = 0.080\ \text{m}

  2. Calculate the flying height above ground level

    The flying height above ground level is the difference between the flying height above sea level (HH) and the average elevation of the terrain (hh).
    Hground=H−h=5500 m−3560 m=1940 mH_{\text{ground}} = H - h = 5500\ \text{m} - 3560\ \text{m} = 1940\ \text{m}

  3. Calculate the scale of the photograph

    The scale (SS) is given by the formula S=f/HgroundS = f / H_{\text{ground}}.
    S=0.080 m1940 mS = \frac{0.080\ \text{m}}{1940\ \text{m}}
    S=0.0000412371134S = 0.0000412371134

  4. Express the scale as a ratio and round

    To express the scale as a ratio of 1:X, we take the reciprocal of the calculated scale.
    X=10.0000412371134=24250X = \frac{1}{0.0000412371134} = 24250

    Rounding this value to the nearest thousand:
    24250≈2400024250 \approx 24000

    The scale of the aerial photograph is:
    1:240001:24000

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