Ideal Launch Angle in Projectile Motion

[ManimalJax]

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I have in my notes that the ideal launch angle in projectile motion is 45 degrees. Next to that note, I have written that it is at this angle that the maximum launch time occurs. Somewhere else in my notes, I have another note that mentions that it is when a projectile is shot at 90 degrees that the maximum amount of time in the air is achieved.

Are these contradictory notes?

 

[DrMattOglesby]

i dont know what max LAUNCH time is.

I do know that max time in air will be achieved with the 90 degree angle though.

The 45 degree angle will achieve the max distance from the launch site.
The time spent in the air with this angle will be less than that of the 90 degree angle.
And, for fun...can you explain to me why this is the case?

 

[BerkReviewTeach]

I have in my notes that the ideal launch angle in projectile motion is 45 degrees. Next to that note, I have written that it is at this angle that the maximum launch time occurs. Somewhere else in my notes, I have another note that mentions that it is when a projectile is shot at 90 degrees that the maximum amount of time in the air is achieved.

Are these contradictory notes?

As the good future doctor Oglesby mentioned, in an ideal situation (same launch and landing elevation, no wind resistance, no spin, etc...), the optimal launch angle is 45 degrees. This is because it is a perfect compromise of flight time (governed by the y-component of the inital velocity, because gravity works in the y-direction) and x-direction speed (because in order to travel horizontally, you have to be moving horizontally).

If the launch angle were 90 degrees, you'd travel straight up and come straight back down, resulting in no net displacement, and thus a range = 0. But, because you had the highest possible y-component for the initial velocity (all of it), you maximized the height to which it climbed and ultimately the time it remained in the air.

To add a third one, if the launch angle was 0 degrees, then it would never leave the ground and range would also be zero (although it would travel, but it would be bowling and not ball tossing).