Question

In a map based on the UTM projection, the grid distance is in error with respect to the geodetic distance by about one in four thousand. If the map distance is 3 cm and the map scale is 1:25,000, then the geodetic distance is ___________m (rounded off to 2 decimal places).

Hint:

In UTM projection, the grid distance slightly differs from the geodetic (true ground) distance. A correction based on the scale factor is often necessary.

Answer 1

Given:

Map distance = 3 cm = 0.03 m
Map scale = 1:25,000
Grid distance is in error by 1 in 4000, i.e., \(\dfrac{1}{4000}\)

First, compute the ground grid distance:
\[ \text{Grid Distance} = 0.03 \times 25000 = 750 \, \text{m} \]

Now, calculate the correction due to scale error:
\[ \text{Error} = \frac{750}{4000} = 0.1875 \, \text{m} \]

Hence, the geodetic distance:
\[ \text{Geodetic Distance} = 750 - 0.1875 = 749.8125 \, \text{m} \]

Final Answer: \(\boxed{749.81 \, \text{m}}\)