How do you define two angles that will result in a range of zero for a projectile launched at an angle to the horizontal?

Oh what a sneaky problem !
The "range" of a projectile is how far out away from the gun it goes before it falls to the ground.
The question is asking you: "What angle should you aim the gun above the horizon so that the bullet doesn't go any distance away from the gun, and it hits the ground exactly where the gun is " And there are two different answers. Really sneaky !
Can you think of how you could fire the gun so that the bullet would hit the ground right under the gun ? How about pointing the gun at the ground ... aiming 90 degrees below the horizon ? That would certainly do it. Is there another way to do it ?
How about aiming the gun straight up in the air ... 90 degrees above
the horizon ? Then it goes up, up, up, runs out of steam, stops rising, starts falling, comes down, down, down, and hits the ground right where the gun was.
As long as there's no air and no wind, the two angles are +90 degrees and -90 degrees above the horizon.
' +90 above ' means straight up. ' -90 above ' means straight down.

Answered by AL2006 | 2024-06-10

To achieve a zero range for a projectile, it can be launched at either 0 degrees (horizontally) or 90 degrees (straight up). Both angles ensure the projectile lands at the same point of launch, resulting in a range of zero. This illustrates the principle of projectile motion with extreme angles leading to no horizontal displacement.
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Answered by AL2006 | 2024-12-26