Your team has been appointed as the search coordinators the state of Nebraska's aerial search and...

 

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Your team has been appointed as the search coordinators the state of Nebraska's aerial search and rescue division. Since Nebraska is so flat, your job should be pretty easy! All you need to do is fly some helicopters over the area and look for whatever you need to look for whatever a given day may call for. Alas, it is not that simple. On any given day, a helicopter pilot can see approximately 2 km in any straight line from the helicopter, so they can see a circle on the ground with radius R km, where R² + h² = 2, where h is the height in kilometers that the helicopter is flying above the ground and is the distance that the pilot can see. Recall that the area of a circle is given as A = R², where R is the radius of the circle. 1. If the pilot wants be able to scan an area of 5 km² at any given time, how high should the pilot be flying? 2. Uh oh! It is foggy out, and now the pilot's visibility has dropped to a mere 0.5 km. Will the pilot be able to scan the same 5 km² of area as they did before? If so, find the height they need to fly at. If not, explain why this won't be possible. 3. Suppose now that the pilot has a pair of binoculars that allows them to see 3 km instead of just 2 km. If the pilot wants to see an area of 5 km², how high do they need to fly? Compare your answer to those in the previous parts. 4. A helicopter's maximum height is 6000 m. Why might it not be the best idea for the pilot to fly at this height if they are trying to conduct a search and rescue operation? Your team has been appointed as the search coordinators the state of Nebraska's aerial search and rescue division. Since Nebraska is so flat, your job should be pretty easy! All you need to do is fly some helicopters over the area and look for whatever you need to look for whatever a given day may call for. Alas, it is not that simple. On any given day, a helicopter pilot can see approximately 2 km in any straight line from the helicopter, so they can see a circle on the ground with radius R km, where R² + h² = 2, where h is the height in kilometers that the helicopter is flying above the ground and is the distance that the pilot can see. Recall that the area of a circle is given as A = R², where R is the radius of the circle. 1. If the pilot wants be able to scan an area of 5 km² at any given time, how high should the pilot be flying? 2. Uh oh! It is foggy out, and now the pilot's visibility has dropped to a mere 0.5 km. Will the pilot be able to scan the same 5 km² of area as they did before? If so, find the height they need to fly at. If not, explain why this won't be possible. 3. Suppose now that the pilot has a pair of binoculars that allows them to see 3 km instead of just 2 km. If the pilot wants to see an area of 5 km², how high do they need to fly? Compare your answer to those in the previous parts. 4. A helicopter's maximum height is 6000 m. Why might it not be the best idea for the pilot to fly at this height if they are trying to conduct a search and rescue operation?

Answer rating: 100% (QA)

1 The pilot should be flying at a height of approximately 447 kilometers above the ground in order t... View the full answer