Question

A staff is held vertical at a distance of 100 m and 300 m, respectively. Observations are taken with a Tacheometer and staff intercepts, with the telescope kept horizontal, are 0.990 m and 3.000 m, respectively. The theodolite is set over a station having a RL of 950.500 m and the height of instrument is 1.425 m. The multiplicative constant of the Tacheometer is __________________ (round off to 2 decimal places).

Hint:

The multiplicative constant of a Tacheometer is calculated using the difference in staff intercepts and the distance between the staff readings.

Answer 1

Correct Answer: 99.1

The formula for the multiplicative constant \( K \) of a Tacheometer is: \[ K = \frac{d_2 - d_1}{\Delta h} \] Where:
- \( d_2 = 300 \, \text{m} \) and \( d_1 = 100 \, \text{m} \) are the distances,
- \( \Delta h = h_2 - h_1 = 3.000 - 0.990 = 2.010 \, \text{m} \) is the difference in staff intercepts.
Now calculate \( K \): \[ K = \frac{300 - 100}{2.010} = \frac{200}{2.010} = 99.505 \] Final Answer: \[ \boxed{99.51} \]