Question

tha motor pumps water from a well 10 m deep and projects it at a speed of 15 meters per second.the water pause ftom the pipe at a rate of 1200 kg per minute calculate the power of the motor ​

Answer 1

4210 W

Step-by-step explanation:

We'll begin by calculating the energy required in lifting the water from the depth. This can be obtained as follow:

Mass (m) = 1200 Kg

Height (h) = 10 m

Acceleration due to gravity (g) = 9.8 m/s²

Energy (E₁) =?

E₁ = mgh

E₁ = 1200 × 9.8 × 10

E₁ = 117600 J

Next, we shall determine the energy required to project the water at 15 m/s. This can be obtained as follow:

Mass (m) = 1200 Kg

Velocity (v) = 15 m/s

Energy (E₂) =?

E₂ = ½mv²

E₂ = ½ × 1200 × 15²

E₂ = 600 × 225

E₂ = 135000 J

Finally, we shall determine the power of the motor. This can be obtained as follow:

Total energy (E) = E₁ + E₂

= 117600 + 135000

= 252600 J

Time (t) = 1 min = 60 s

Power (P) =?

P = E/t

P = 252600 / 60

P = 4210 W

Therefore, the power of the motor is 4210 W.