Vectors and Projectiles - Mission VP10 Detailed Help

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Several projectiles are launched from ground height with the same launch speeds and varying angles between 0 degrees and 90 degrees with the horizontal. The projectile launched at ___ degrees would remain in the air the longest. The projectile launched at ___ degrees would have the greatest horizontal displacement. The projectile launched at ___ degrees would have the same horizontal displacement as the projectile launched at 20 degrees.

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For an angled-launched projectile, the vertical distance of rise and the time of flight is dependent upon vertical parameters of motion. The most important variable to effect the peak height and time of flight is the original vertical velocity (voy). The horizontal displacement is dependent upon both the time of flight and the original horizontal velocity (vox). For the same launch speeds, the projectile with the greatest angle of launch will have the greatest time of flight, yet its horizontal velocity is too small to provide the maximum horizontal displacement. A lengthy derivation could be performed to show which angle optimizes the combined effect of time of flight and horizontal velocity. Yet a picture, being worth a 1000 words, provides a better illustration. Either of the links in the Hot Link section leads to a page with an animation of the trajectory of three projectiles with different launch angles. The discussion that accompanies the animation provides a thorough discussion of the question.

What angle of launch would maximize the range (horizontal displacement) of a projectile? What affect does the angle of launch have upon the range (horizontal displacement) of a projectile? What angle of launch would maximize the time of flight of a projectile?