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Question
Unreasonable Results (a) Find the maximum range of a super cannon that has a muzzle velocity of 4.0 km/s. (b) What is unreasonable about the range you found? (c) Is the premise unreasonable or is the available equation inapplicable? Explain your answer. (d) If such a muzzle velocity could be obtained, discuss the effects of air resistance, thinning air with altitude, and the curvature of the Earth on the range of the super cannon.
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Final Answer
  1. $1600 \textrm{ km}$
  2. ]

  3. The range formula doesn't apply very well. It is based on assumptions that are not true in this circumstance.
    1. Flat Earth Assumption: curvature of the Earth can't be neglected on a 160 km scale. Range will actually be larger.
    2. Air resistance: since drag force is proportional to the square of the velocity, the very large muzzle velocity will result in very significant drag forces. The range will be significantly shorter.
    3. Constant air density assumption: Air density decreases with height. Range will be longer as a result.
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OpenStax College Physics Solution, Chapter 3, Problem 50 (Problems & Exercises) (3:18)

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