Problem 1
A projectile is launched from level ground at speed and angle above horizontal; neglect air resistance. Find its range and the angle giving maximum range; gravity is . Treat the projectile as a point mass returning to its launch height; take vertical upward as positive and neglect drag. (a) Find the flight time and range . (b) For fixed , find the launch angle and maximum range. (c) Find the maximum height for a general launch angle. Express each answer in terms of the supplied parameters, using SI units for any numerical evaluation. State the assumptions used, check dimensions at each result, and compare with the governing law to catch a sign error or a missing condition.
problems.proof.stepOf
problems.proof.analysis
The next equation adds the relevant constraint or conservation law. Without it, the variables would not be linked and the system could not be solved consistently.
problems.proof.pitfall. Do not omit the sign convention or the model’s physical condition; check the limiting case before accepting a solution.