GATE Papers >> Civil >> 2018 >> Question No 46

Question No. 46
A square area (on the surface of the earth) with side 100 m and uniform height, appears as 1 cm2 on a vertical aerial photograph. The topographic map shows that a contour of 650 m passes through the area. If focal length of the camera lens is 150 mm, the height from which the aerial photograph was taken, is

Answer : (C) 2150 m

Solution of Question No 46 of GATE 2018 Civil Paper

Actual area = 100 x 100 = 104 m2

Area on the map = 1 cm2 = 10-4 m2

Elevation of the surface = 650 m

Focal length of camera, f = 150 mm

Scale of the photograph,

$\begin{array}{l}\mathrm S=\sqrt{\frac{10^{-4}}{10^4}}=\frac1{10^4}\\\mathrm S=\frac{\mathrm f}{\mathrm H-\mathrm h}\\\frac1{10^4}=\frac{150\times10^3}{\mathrm H-650}\\\mathrm H=1500+650=2150\;\mathrm m\;\end{array}$

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