Moderate wind speeds:
a. at least 5
b. gusting up to 30
c. in the range of 10-40
d. sustained at 40
mph provide suitable power without overfatiguing components.
Answer (2)
The best definition of moderate wind speeds for power generation is option (c): in the range of 10-40 mph. This range is optimal to ensure efficiency without risking damage to components. Other options either present too broad of a definition or refer to gusts, which are not suitable for sustained power generation.
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The problem asks to identify the best description of moderate wind speeds from the given options.
Option (a) is too broad.
Option (b) refers to wind gusts, not sustained speed.
Option (c) provides a reasonable range of 10-40 mph.
Option (d) specifies a single speed of 40 mph. Therefore, the best answer is c .
Explanation
Understanding the Problem We are given four conditions for moderate wind speeds: a. at least 5 mph b. gusting up to 30 mph c. in the range of 10-40 mph d. sustained at 40 mph We need to determine which of these conditions, or combination of conditions, best describes moderate wind speeds suitable for power generation without overfatiguing components.
Analyzing Each Condition Let's analyze each condition: a. at least 5 mph: This means the wind speed w must satisfy wl ess 5 .
b. gusting up to 30 mph: This means the wind gusts g must satisfy g ≤ 30 . This condition refers to gusts, not sustained wind speed. c. in the range of 10-40 mph: This means the wind speed w must satisfy 10 l ess wl ess 40 .
d. sustained at 40 mph: This means the wind speed w is constantly 40 mph, i.e., w = 40 .
Considering the Implications Now let's consider the implications of each condition:
Condition (a) alone is too broad. Wind speeds of 5 mph might not be sufficient for efficient power generation.
Condition (b) refers to wind gusts, which are short bursts of high speed. While important for structural design, it doesn't define moderate sustained wind speed.
Condition (c) provides a reasonable range for moderate wind speeds. It excludes very low speeds (below 10 mph) and very high speeds (above 40 mph).
Condition (d) specifies a single sustained speed of 40 mph. While this might be suitable, it doesn't account for variations in wind speed.
Determining the Most Suitable Description Considering all conditions, the most suitable description of moderate wind speeds is given by condition (c), which states that the wind speed should be in the range of 10-40 mph. This range provides a balance between sufficient power generation and avoiding overfatigue of components.
Final Answer Therefore, the answer is (c).
Examples
Understanding wind speed ranges is crucial in various applications, such as wind energy generation, aviation, and weather forecasting. For instance, in wind energy, knowing the optimal wind speed range helps in designing efficient wind turbines that can harness maximum power without experiencing excessive wear and tear. Similarly, in aviation, pilots need to be aware of wind speeds to ensure safe takeoffs and landings. In weather forecasting, predicting wind speeds is essential for issuing warnings about potential hazards like strong winds or storms. This problem demonstrates how mathematical concepts like inequalities and ranges can be applied to real-world scenarios involving wind speed analysis.
