GATE-2018 (24) :Wyllie – Time average equation

Problem

2.A runway  measures 5 cm on an airphoto but measures 500 m on the ground. The elevation of the runway is 1000 m MSL. If the focal length of the camera is 150 mm, what is the altitude of the aircraft?

Solution:

Scale = photo distance / ground distance = f/ (H-h)

photo distance = 5cm = 50 mm

ground distance = 500m = 500000 mm

focal length (f) = 150 mm

The elevation of the runway (h) = 1000m

                                                   = 1000000 mm

Therefore,

==> 50/ 500000 = 150 / (H- 1000000)

==> 1/ 10000 = 150 / (H-1000000)

==> H-1000000 = 150 *10000

==> H= 1500000 + 1000000

==> H= 2500000 mm

==> H= 2500 m

The altitude of the aircraft (or) camera height (H) = 2500 m