The stooping hawk

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Hawks and gannets soar above the ground and, when they spot prey, they fold their wings and essentially drop like a stone. They have evolved a highly aerodynamic shape that lets gravity build up their speed without having to make the effort of trying to fly at a high speed. (See the figure of a diving hawk at the right. The technical term for this maneuver is “stooping”.) For this problem, you may approximate the strength of the gravitational field as $g = 10 \text{ N/kg}$.

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1. If a hawk is slowly soaring at a height of about 150 meters and spots a vole on the ground, folds its wings and begins its dive, it will simply accelerate downward with the gravitational acceleration, $10 \text{ m/s}^2$. With what speed will it be going when it gets to the ground? (Of course, it has to turn a bit above the ground in order not to crash. We will ignore this part of its flight path.)  

2.  If the vole on the ground has been nervously watching the hawk, how much time does it have to get away from the instant it observes the hawk pulling in its wings?  

3. If the vole can run at a speed of $2 \text{ m/s}$ and always wants to be safe, how close to a safe hole should it always stay?

4. What assumptions did you need to make to solve this problem? Is it reasonable to make them? 

Image Source: Wikimedia
Commons, public domain

Joe Redish 1/15/13