Projectile Motion from TBR

[DeathandTaxes]

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Can anyone explain to me why in this scenario maximum height is NOT at 45 degrees?


The answer is B, but I assumed D because of this fact.

 

[el_duderino]

We can rule out A because we know that at 0 degrees, the spheres would still travel some distance.

We can rule out D because.... well, it doesn't make much sense. You're looking at, what, a 4th-order relationship there? No reason you'd have something that looked like that.

The reason the max height is not reached at 45 degrees is because of the height advantage by shooting off a cliff. You want more of the velocity in the horizontal direction to take better advantage of the extra 100 meters of height you already have.

The part that confuses me is that at 90 degrees we should have a range of 0, but neither B nor C have that. But I'd choose B because of the cliff.

 

[graden]

Basically if the elevation isn't equal, 45 degrees isn't max range anymore and anything less is, because horizontal velocity takes advantage of more time in the air.

edit: jonnythan worded it better than me.

 

[el_duderino]

I credit Angry Birds for helping me work that problem out.

 

[Lunasly]

We can rule out A because we know that at 0 degrees, the spheres would still travel some distance.

We can rule out D because.... well, it doesn't make much sense. You're looking at, what, a 4th-order relationship there? No reason you'd have something that looked like that.

The reason the max height is not reached at 45 degrees is because of the height advantage by shooting off a cliff. You want more of the velocity in the horizontal direction to take better advantage of the extra 100 meters of height you already have.

The part that confuses me is that at 90 degrees we should have a range of 0, but neither B nor C have that. But I'd choose B because of the cliff.

That's a good analysis. It is also to my understand that max range is achieved at 45 degrees only when you shoot a projectile from a level surface. Since we are at a height, the length of time that the projectile is in the air will also now have a large impact on its range (as total time of flight increases). Total time of flight is increased if we increased the maximum height of the projectile. If the projectile is launched at 30 degrees, it will achieve a higher maximum height compared to if it were launched at either 45 degrees and 60 degrees, respectively. This principle is intuitive. I might be wrong here, but another reason as to why I would not pick D is because of the shape of the graph.

I am also confused as to why the range is not 0 if it is launched from 90 degrees. The passage does claim that winds are negligible, however, maybe they do have a slight affect?

 

[neurodoc]

I am also confused as to why the range is not 0 if it is launched from 90 degrees. The passage does claim that winds are negligible, however, maybe they do have a slight affect?

I guess that the slingshot bars are set right at the edge of the cliff and if shot directly upwards the ball will drop down the cliff to the water below, travelling some distance.
Also note that the y-axis is range not height plotted against initial take-off angle. What they mean by range is not completely clear and therefore the question is confusing. They may mean total distance traveled by the projectile or just the horizontal distance (i.e. how far away from the cliff it lands in the water). In either case, D is definitely incorrect because it is not parabolic. As has been said, the horizontal distance travelled by the projectile is maximized at 45 deg take-off when shot from level terrain. But it is being shot from the edge of a cliff 100m above the water, so it will travel a greater horizontal distance. The question is which of the three remaining choices is the best answer? A can be eliminated if we assume that at 0 and 90 deg takeoff angles there is some non-zero range for the experimental conditions (for the reason I mentioned above). That leaves B & C. To choose between them you need to consider that the horizontal velocity component is going to extend the projectile's range and that component is greater for angles less than 45 deg compared to angles greater than 45 deg. That's why B is the "best" answer, but frankly I think that this is a poorly worded question. In fact, I think that one could argue that the greatest range would be achieved by launching the projectile at exactly 45 deg, but they don't supply a graph that fits the other conditions of the experiment that require non-zero ranges for 0 and 90 deg take-off angles....