a vertical photograph was taken with a camera of focal length f 152 mm from a flying height of 3000 m above mean ground level. Images of the top T and the base B of a tower are at 61.5 mm and 62 mmrespectively from the principal point, given that the base elevation of the tower was 1200 m above datum, calculate the height of the tower
Question
a vertical photograph was taken with a camera of focal length f 152 mm from a flying height of 3000 m above mean ground level. Images of the top T and the base B of a tower are at 61.5 mm and 62 mmrespectively from the principal point, given that the base elevation of the tower was 1200 m above datum, calculate the height of the tower
Solution
To calculate the height of the tower, we can use the concept of similar triangles.
Step 1: Determine the distance between the top and base of the tower in the image. The distance between the top T and the base B of the tower in the image is given as 61.5 mm - 62 mm = -0.5 mm.
Step 2: Convert the distance in the image to the actual distance on the ground. We can use the formula: (actual distance) / (focal length) = (image distance) / (height of camera above ground) Let's substitute the given values: (actual distance) / 152 mm = -0.5 mm / 3000 m Simplifying, we get: (actual distance) = (-0.5 mm / 3000 m) * 152 mm (actual distance) = -0.253333 mm
Step 3: Calculate the height of the tower. We can use the formula: (height of tower) / (actual distance) = (height of camera above ground) / (focal length) Let's substitute the given values: (height of tower) / -0.253333 mm = 3000 m / 152 mm Simplifying, we get: (height of tower) = (-0.253333 mm * 3000 m) / 152 mm (height of tower) = -4.999 m
Since the height of the tower cannot be negative, we can conclude that the height of the tower is approximately 4.999 meters.
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