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With the drag constant k = 0.0089 per metre, find the best angle (whole degrees, from 20 to 70) for…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
With the drag constant per metre, find the best angle (whole degrees, from 20 to 70) for the speeds 20, 40 and 60 m/s. Compare the range with the range without air, . Explain the trend of the best angle.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Plan. For each speed, compute the range for every angle with solve_ivp, and take the angle with the largest range.
Check. The results are: 20 m/s, 43 degrees, 32.2 m (without air 40.8 m). 40 m/s, 40 degrees, 83.5 m (163.3 m). 60 m/s, 37 degrees, 125.3 m (367.3 m).
Answer: the best angle falls as the speed grows: 43, 40 and 37 degrees. The drag grows with the square of the speed, so at a high speed the air matters more, and a flatter throw, which spends less time in the air, is better. At 60 m/s the air takes away two thirds of the range.
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