An oblique aerial photograph of a cricket stadium is taken which includes two linear practice pitches (p and q). The length of both the pitches measured on ground is \( 15\ \text{m} \). The dimension of the image is \( 230\ \text{mm} \times 230\ \text{mm} \), while the photo lengths of p and q are \( 5\ \text{mm} \) and \( 15\ \text{mm} \), respectively.
What are the photo scales for p and q, respectively?
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Photo scale for a line equals photo length divided by the true ground length of that line; compute it separately for pitch p and pitch q.
Step 1: Convert the ground length to centimetres. The true ground length of each pitch is $15\ \text{m} = 1500\ \text{cm}$. Working in centimetres avoids repeated zeros and gives a convenient cross check. Step 2: Convert the photo lengths to centimetres. Photo length of p $= 5\ \text{mm} = 0.5\ \text{cm}$. Photo length of q $= 15\ \text{mm} = 1.5\ \text{cm}$. Step 3: Form the representative fraction for p. \[ \text{RF}_p = \frac{\text{photo length}}{\text{ground length}} = \frac{0.5}{1500} = \frac{1}{3000} \] Step 4: Form the representative fraction for q. \[ \text{RF}_q = \frac{1.5}{1500} = \frac{1}{1000} \] Step 5: Confirm the image format size is irrelevant to this calculation. The $230\ \text{mm} \times 230\ \text{mm}$ format is the size of the film/sensor; it does not enter the scale calculation for individual lines, since scale only depends on the ratio of the measured photo length to the true ground length of that particular line.\[ \boxed{S_p = \tfrac{1}{3000},\ S_q = \tfrac{1}{1000}} \]
