During a fieldwork measurement along a baseline, a geography student uses a steel tape wit… — JAMB UTME

During a fieldwork measurement along a baseline, a geography student uses a steel tape with a nominal length of $30.00\text{ m}$ . Due to high ambient temperature, the actual length of the tape has expanded to $30.15\text{ m}$ . If the uncorrected recorded distance for the baseline is $450.00\text{ m}$ , what is the true ground distance and the nature of the measurement error?

The true ground distance is $452.25\text{ m}$ , representing a cumulative negative error.Answer
B
The true ground distance is $447.75\text{ m}$ , representing a cumulative positive error.
C
The true ground distance is $452.25\text{ m}$ , representing a compensatory positive error.
D
The true ground distance is $447.75\text{ m}$ , representing a random field error.

Answer

The true ground distance is

452.25\text{ m}

, representing a cumulative negative error.

The correct answer states that the true ground distance is

452.25\text{ m}

and represents a cumulative negative error. When a

30.00\text{ m}

tape expands to

30.15\text{ m}

, every time the tape is laid out,

30.15\text{ m}

of ground is covered, but only

30.00\text{ m}

is added to the tally. Multiplying

450.00\text{ m}

by the ratio

30.15 / 30.00

gives a true ground distance of

452.25\text{ m}

. Because the recorded distance is shorter than the actual ground distance, the error is negative, and because it acts consistently in one direction throughout the survey, it is cumulative.

Step-by-Step Solution

Determine the total number of tape applications made during the baseline measurement.

Number of applications

N = \frac{450.00\text{ m}}{30.00\text{ m}} = 15

The recorded distance is measured in standard

30.00\text{ m}

units.

Calculate the true ground distance using the actual expanded length of the tape.

True Distance

= 15 \times 30.15\text{ m} = 452.25\text{ m}

(or using

L_{\text{true}} = L_{\text{recorded}} \times \frac{l'}{l} = 450.00 \times \frac{30.15}{30.00} = 452.25\text{ m}

Each application of the expanded tape spans

30.15\text{ m}

of ground, while only

30.00\text{ m}

is recorded.

Classify the nature and sign of the survey error.

The recorded measurement is

2.25\text{ m}

less than the true distance (

450.00\text{ m} < 452.25\text{ m}

). The error in the recorded distance is negative and accumulates proportionally with line length, making it a cumulative negative error.

When a measuring tape is too long, the recorded distance is always less than the true distance, causing a cumulative negative error.

Key Concept

Tape Length Error Corrections & Cumulative vs. Compensatory Errors

Estimated Time:2m 0s

Question

Answer

Step-by-Step Solution

Key Concept

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