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.Cevap
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.

Cevap

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.

Adım Adım Çözüm

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.

Anahtar Kavram

Tape Length Error Corrections & Cumulative vs. Compensatory Errors

Tahmini Süre:2m 0s

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