Question

a fire hose held near the ground shoots water at a speed of 6.5 m/s. at what angle(s) should the nozle point in order that the water land 2.0 m away, why are there two different angles?

in the diagram, the hose is held straight up at theta degrees going at 6.5 m/s and with water falling down.. the distance between initial and final water displacement is 2m.. a fire hose held near the ground shoots water at a speed of 6.5 m/s. at what angle(s) should the nozle point in order that the water land 2.0 m away, why are there two different angles?

Answer 1

There are two trajectories a projectile can travel to reach a destination, the high and low orbit.
The furthest destination can be obtained with an angle of Theta = 45°.
The high and low orbit are obtained with equal angles away from this Theta: Theta1 = 45°+Phi (high orbit) and Theta2 = 45°-Phi (low orbit).


formula for the inclined throw
\[x _{m}=\left( v _{0}^{2}\sin \left(2.\Theta\right) \over g \right)\]
solving for Theta gives
Theta = 13,83 °
or
Theta = 90°-13,83° = 76,17°
(See of it as mirrorred around the 45° axis.

Answer 2

sorry : mirrored

Answer 3

i dont understand

Answer 4

Sorry, I will tell you how I came to that:
Water that comes out of a hose are actually only water drops with much the same speed and direction. The beam that the water forms, are only water drops that have a coherence, we call laminar streaming . The water drops that leave the water hose have an initial speed at the nozzle. I make an approximation by supposing the angle between the horizontal at the nozzle and the horizontal 2 meter further being zero, which I suppose I can do for answering this problem (it's like saying that the earth is flat, sort of speak). If the hose is pointed in any upwards direction from the earth's surface, the speed of the water drops decreases until the water drops reach a climax height and return to the earth surface with increasing speed, until the drops join the earth's surface (if you think about this, this speed at dropping point is equal to the initial speed, if it were not for the friction with the air. The speed is slower when the drops of water hit the ground, because they heated the air and themselves by friction) . Now, the paths that all these drops follow can be described by geometric figures, with mathematical equations: they follow the path of a parabola, with a quadratic equation.
To analyse and quantise the trajectories I can use the scientific method of Rene Descartes and use an orthogonal axis structure with origin at the point of the nozzle, and the horizontal axis parallel to the ground, and the vertical axis straight upwards to the beautiful sky. We may call the axes X and Y, just like you probably saw somewhere before, but we can use any symbol for naming the axes. (orthogonal means 'straight angle', thus axes have straight angle to one another).