A 100 ft steel tape, standardized at 68°F and supported throughout under a tension of 10 lbs, was found to be 100.2 ft long. The tape has a cross-sectional area of 0.009 in² and a weight of 0.03 lb/ft. The tape is used to measure a horizontal distance (AB), and the measured length comes out to be 300 ft.

Caltrans plans a new ramp to connect Nutwood with US57. The ramp starts from point A (on Nutwood) to point C (on US57), with point C vertically above point B (a current point on Nutwood that will get buried by the ramp). The ramp must have a smooth 4% grade, thus the tape will be used fully supported.

Determine the correct slope distance to be measured (i.e., length AC) if a pull of 15 lbs is used, and the temperature is 96°F.

A) 301.9 ft
B) 302.5 ft
C) 299.6 ft
D) 300.2 ft

To determine the correct slope distance (length AC) using a 100 ft steel tape supported under 15 lbs of tension at 96 °F, we need to follow these steps:

1. Calculate the correction for tape length due to the change in tension from 10 lbs to 15 lbs:

- Calculate the correction factor (CF) using the formula:

CF = (T2 - T1) / T1

CF = (15 - 10) / 10

CF = 0.5

2. Calculate the correction for tape length due to the change in temperature from 68 °F to 96 °F:

- Calculate the coefficient of thermal expansion (α) for steel tape:

α = 6.5 x 10^-6 / °F

- Calculate the temperature correction factor (TCF) using the formula:

TCF = α x L x ΔT

TCF = 6.5 x 10^-6 x 100 x (96 - 68)

TCF = 0.208 ft

3. Calculate the corrected length of the tape:

- Corrected length = Original length + CF x Original length + TCF

- Corrected length = 100.2 + 0.5 x 100.2 + 0.208

- Corrected length = 100.2 + 50.1 + 0.208

- Corrected length = 150.308 ft

4. Calculate the corrected slope distance (length AC) using the corrected tape length:

- Slope distance (length AC) = Measured distance / (Corrected length / Original length)

- Slope distance = 300 / (150.308 / 100)

- Slope distance = 300 / 1.50308

- Slope distance ≈ 199.5 ft

Therefore, the correct slope distance to be measured (length AC) is approximately 199.5 ft. This value is not provided in the answer choices given.

So, none of the given option is correct