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 ___________

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

Correct Answer: 749.79

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: \[ {Grid Distance} = 0.03 \times 25000 = 750 { m} \] Now, calculate the correction due to scale error: \[ {Error} = \frac{750}{4000} = 0.1875 { m} \] Hence, the geodetic distance: \[ {Geodetic Distance} = 750 - 0.1875 = 749.8125 { m} \]