Question

1. the point of intersection of the center line of elm rd. with the center line of first st. was originally recorded (using a 30 - m steel tape) as being at 6 + 11.23. how far from the existing station mark 5 + 00 on first st. would a surveyor have to measure along the center line to reestablish the intersection point under the following conditions? temperature to be - 6°c, with a tape that is 29.995 m under standard conditions.

Explanation:

Step1: Calculate the distance from the origin - station mark

The original intersection point is at $6 + 11.23$ and the station mark is at $5+00$. The distance $L_0$ between them in the original measurement is $(6\times100 + 11.23)-(5\times100)=111.23$ m.

Step2: Determine the correction factor for the tape

The nominal length of the tape $L_n = 30$ m and the actual length of the tape under - standard conditions $L_a=29.995$ m. The correction per tape length $\Delta L$ is $L_a - L_n=29.995 - 30=- 0.005$ m.

Step3: Calculate the corrected distance

The number of tape - lengths $n=\frac{L_0}{L_n}=\frac{111.23}{30}\approx3.7077$. The total correction $\Delta L_{total}=n\times\Delta L=3.7077\times(-0.005)= - 0.0185385$ m. The corrected distance $L = L_0+\Delta L_{total}=111.23-0.0185385 = 111.2114615\approx111.21$ m.

Answer:

$111.21$ m