For projectile motion in the absence of air resistance, you learned in General Physics I that the horizontal range of a projectile is a maximum at 45o. Furthermore, the range is the same (but smaller than the maximum) for two angles, equally above as below 45o. (For example, 47o and 43o yield the same range.) This can be understood qualitatively. For a given angle below 45o, the initial vertical velocity is smaller and the total flight time is also smaller. But the horizontal velocity is larger. For the same angle above 45o, the vertical velocity and hence time of flight is larger, but the horizontal velocity is smaller. Without air resistance, these two effects result in the same horizontal range. Now consider a similar argument applied to the problem with air resistance. Air resistance increases with increasing speed and decreases with decreasing speed. The symmetry of the argument is broken. Considering the presence of air resistance, do you think the angle for maximum range will be above, below, or still at 45o? Be sure to justify your choice!
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