a fire hose held near the ground shoots water at a speed of 6.4m/s, at what angle should
In order to determine the angle at which the fire hose should be held, we can make use of the principles of projectile motion.
The horizontal and vertical components of the water's velocity must be considered separately. The horizontal velocity remains constant as there is no acceleration in that direction. In this case, it is given as 6.4 m/s.
However, the vertical velocity will be affected by gravity. At the highest point of the water's trajectory, the vertical velocity will become zero. Using this information, we can determine the angle.
Let's break down the process step-by-step:
1. Identify the knowns and unknowns:
- Knowns: horizontal velocity (6.4 m/s), acceleration due to gravity (9.8 m/s^2)
- Unknown: angle of projection
2. Analyze the vertical component of the water's velocity:
- The initial vertical velocity (v₀y) is given as zero at the maximum height.
- The final vertical velocity (vfy) will also be zero at the highest point.
3. Use the kinematic equation to find the time taken to reach the highest point of the trajectory (t):
- vf = v₀ + at
- Rearranging the equation: vfy = v₀y + gt
- Since vfy is zero: 0 = 0 + 9.8t
- Solving for t, we get t = 0 seconds.
4. Calculate the time taken to reach the highest point using the horizontal component of the velocity:
- The horizontal and vertical velocities are independent of each other.
- Since the vertical velocity is zero throughout the motion, we can use the horizontal velocity (v₀x) and distance (range) to find the time (t):
- Range = v₀x * t
- Range = 6.4 * t
- Remember, t = 0 from the previous calculation.
- Therefore, the time taken to reach the highest point is also 0 seconds.
5. Calculate the angle of projection (θ):
- tan(θ) = (v₀y / v₀x)
- tan(θ) = 0 / 6.4
- Since the numerator is zero, the angle (θ) must also be zero degrees.
In conclusion, to shoot water at a speed of 6.4 m/s near the ground, the fire hose should be held parallel to the ground, or at an angle of 0 degrees.