Final answer:
To find the speed of water flow at point 1, use the conservation of energy principle and the equation for projectile motion. The initial speed of flow required to reach the plant 6.10 m away can be calculated using the equation for projectile motion. The speed of flow in the hose can be found using the volume flow rate and the cross-sectional area of the hose.
Step-by-step explanation:
Calculating the Speed of Water Flow
- Calculate the initial speed of water flow using the volume flow rate and the cross-sectional area of the hose.
- Calculate the speed of water flow at point 1 by using the conservation of energy principle (taking into account the change in height and the distance).
- Use the equation for projectile motion to find the initial speed of flow required to reach the plant 6.10 m away.
- Calculate the speed of water flow in the hose using the cross-sectional area and the volume flow rate.
To find the speed of water flow at point 1:
Speed at point 1, v1 = √(2 * g * h)
Where g is the acceleration due to gravity (9.8 m/s²) and h is the height (1.0 m).
To find the initial speed of flow required to reach the plant 6.10 m away:
Using the equation for projectile motion, the initial speed of flow, v_initial, can be found using the following equation:
v_initial = √((d * g) / (2 * sin(2θ)))
Where d is the horizontal distance (6.10 m) and θ is the angle of projection (45°).
To find the speed of water flow in the hose:
Speed in the hose, v_hose = Q / A
Where Q is the volume flow rate (0.10 m³/min) and A is the cross-sectional area of the hose (π * r²).
By substituting the given values into the equations above, you can calculate the speed of water flow at point 1 and the speed of flow in the hose.