An engineer needs to determine the distance across a rive whose banks are approx. parallel. Standing on one side of the bank, the engineer can see the other side. The engineer only has a 30 foot measuring tape ( which is shorter than the distance from one bank to the other) What is a procedure to determine the approximate distance across the river?
To determine the approximate distance across the river using a 30-foot measuring tape, the engineer can follow the following procedure:
1. Find a point on the same side of the river where the opposite bank aligns with a specific landmark or object.
2. Measure the distance from the starting point to the landmark/object using the 30-foot measuring tape.
3. Move along the riverbank, keeping the landmark/object aligned with the opposite bank as much as possible.
4. After moving some distance, measure the new distance from the starting point to the landmark/object using the measuring tape.
5. Note the total distance covered from the starting point and the difference in measured distances.
6. Use the proportion method to calculate the approximate distance across the river:
River width / Total distance covered = Difference in measured distances / Measuring tape length
(River width * Measuring tape length) / Difference in measured distances = Total distance covered
River width ≈ (Total distance covered * Difference in measured distances) / Measuring tape length
By following this procedure, the engineer can estimate the approximate distance across the river using the available measuring tape. It is important to keep in mind that this method can introduce some degree of error, so the result will be an approximation.
To determine the approximate distance across the river without having a measuring tape long enough, the engineer can use the following procedure:
1. Find a point on the same side of the river that aligns with the opposite bank and is directly across from the position where the engineer is standing. This can be achieved by using landmarks or visual cues.
2. Measure the distance from where the engineer is standing to the chosen point using the 30-foot measuring tape. Let's call this distance "A".
3. Next, find a second point on the same side of the river, aligned with the opposite bank, but at a different position from the first point. This new point should be far enough from the first point so that when the engineer stands on this point, they can clearly see the intersection of the opposite bank with an imaginary line connecting the two points.
4. Measure the distance from the second point to the intersection of the opposite bank using the 30-foot measuring tape. Let's call this distance "B".
5. Now, the engineer needs to calculate the ratio of "A" to "B". Since they know the actual distance between the two points on the selected side of the river (30 feet), they can use this ratio to estimate the distance across the river.
6. Assuming distance "B" is smaller than "A" (which is likely), the engineer can use the following formula to estimate the distance across the river ("D"):
D ≈ (B / A) * 30 feet
7. Plug in the measured values into the formula to calculate the estimated distance across the river.
It's important to note that the accuracy of this method depends on the engineer's ability to choose points on the same side that align with the opposite bank accurately. The accuracy is also influenced by the precision of the measurements made with the 30-foot measuring tape.