When a projectile is shot at ground level the range formula is this...
d = (v2/g) * sin 2*theta
d=range
v=velocity
g=speed of gravity
sin= sine function
theta=angle that you make when the projectile is shot
In your question you are asking about theta. The maximum distance you will get is when theta is 45 degrees. This is because of gravity. Gravity is pulling down on the object. When something is shot above 45 degrees gravity pull down on the object the same way as it pulls down on the corresponding angle below 45 degrees. When I say corresponding angle look below. Basically the answer to your question is because of gravity.
Corresponding angles...
44 and 46
50 and 40
10 and 80
15 and 75
89 and 1
30 and 60
90 and 0
If you notice they all add up to 90 degrees. 90 degrees is the highest angle that can be shot. If it is greater than 90 degrees then the projectile will go behind you.
because 30 and 60 makes 90
The interior angles can have any value in the range (0, 360) except 180 degrees and the same for the exterior angles. The only constraint is that the sum of the exterior angles is 360 degrees.
Congruent angles (or equivalent angles) have the same angle measure.
they are the opposite of same side interior angles
Angles are equal or congruent to each other when the measurements of the angles are the same.
For a projectile launched at an angle θ, the range is the same for angles of θ and (90-θ) degrees. This is because the horizontal and vertical components of the initial velocity are the same for these angles, resulting in the same horizontal range.
It is a case of Trigonometry/Geometry. The two triangles formed by the angles and sides of artillery aiming are "Similar" (not congruent) since two angles and a side (base) are Similar. Because the Range of the projectile is 2x the base (which is congruent) of the triangles, the range MUST be the same.
If the question is in the context of the flight of a projectile, the answer is none.
Two different angles can lead to the same range because the same horizontal distance can be covered by projectiles launched at different launch angles. The range of a projectile is influenced by both its initial velocity and the launch angle. When two different launch angles result in the same horizontal distance traveled, it means that despite the difference in trajectory, the vertical and horizontal components of the motion combine in such a way that the projectile lands at the same distance.
The launch angle and initial speed of a projectile are both factors that determine the range and height of the projectile. A higher launch angle with the same initial speed will typically result in a longer range but lower maximum height. Conversely, a lower launch angle with the same initial speed will result in a shorter range but a higher maximum height.
If "range" means that the shooter and the target are on the same level: quadrupled (if airesistance can be neglected). It takes twice the time until gravity "eats up" vertical velocity and during that time the projectile moves with double horisontal velocity. But if you shoot horisontally from a cliff at double velocity the flighttime will be the same and the range only doubled.
For a projectile launched at a certain speed, an angle of launch that is complementary to the original angle (i.e., the sum of the two angles is 90 degrees) would result in the projectile landing at the same distance. This is due to the symmetrical nature of the projectile's trajectory in a vacuum without air resistance.
w2hen the angle of projection is larger than 45 degree the height attained will be more but the range is again less.in this case angle is 30 degree which is less than 45 degree and 60 degree angle is greater than angle of 45 degree which have less range and is equal to range of 30 degree .so ranges are equal.
For the projectile to land at the same distance with the same initial speed, it must be launched at an angle of 15 degrees from the horizontal. This is because the range of a projectile is maximized when launched at a 45-degree angle. So, launching at 15 degrees in the opposite direction of 75 degrees should bring the projectile to the same landing point.
At a certain angle - 45 degrees if the starting point and end point are at the same level, and air resistance can be ignored - and at a certain speed, the range is maximum. Both for lower and for higher angles, you get a lower range.
They are dimensionally similar, but they are not exactly the same. There are differences in projectile grains and neck angles - the latter can cause improper headspacing if used in a chamber not intended for that cartridge.
No. The range of the projectile thrown at 90 degrees is 0. It goes straight up and then straight down!