Final answer:
To determine the angles at which a fire hose nozzle should be pointed for the water to land 2.0 meters away, we use projectile motion equations and find that the water should be launched at approximately 15.5 degrees or 73.5 degrees from the horizontal.
Step-by-step explanation:
Calculating the Angle for Projectile Water from a Hose
The question at hand involves finding the angle at which a fire hose nozzle should be pointed to shoot water so that it lands 2.0 meters away. This is a classic physics problem involving projectile motion. To solve this, we can use the kinematic equations for projectiles launched at an angle.
For water shot from a hose with a velocity (v) of 6.0 m/s to land 2.0 m away, we need to find the angle(s) at which the nozzle should be pointed. There are typically two angles that will result in the water landing at the same distance: a shallower angle and a steeper angle.
The horizontal range (R) of a projectile is given by R = (v^2 * sin(2 * θ)) / g, where θ is the launch angle and g is the acceleration due to gravity, which is approximately 9.81 m/s^2. Plugging in the numbers we get:
R = (6.0^2 * sin(2 * θ)) / 9.81
To find the angles, we set R to 2.0 m and solve for θ:
2.0 = (36 * sin(2 * θ)) / 9.81
Solving for sin(2 * θ) gives us:
sin(2 * θ) = (2.0 * 9.81) / 36
sin(2 * θ) = 0.545
Now, using a calculator, we find that 2 * θ = 33 degrees or 147 degrees. Thus, the two possible angles are approximately θ15.5 degrees or θ73.5 degrees. These are the launch angles at which the water will land 2.0 m away.