an engine pumps out 40 kg of water in one rawnd the water comes out vertically upward with a velocity of 3m/s what is the power of engine in kilowatt
(A).1200KW(B).120KW(C).12KW(D).1.2KW
1.2
Explain plz
1.2
To find the power of the engine, we need to calculate the work done by the engine in pumping out the water.
Work is given by the formula: Work = Force × Distance × Cos(θ)
In this case, the force is the weight of the water, distance is the height the water is being pumped, and θ is the angle between the force and the displacement (which is 0 degrees because the water is coming out vertically upward).
Weight of an object is given by the formula: Weight = mass × gravity
Here, the mass of water pumped out in one round is given as 40 kg.
We can assume that the acceleration due to gravity is 9.8 m/s².
So, the weight of the water is: Weight = 40 kg × 9.8 m/s²
Next, we calculate the work done:
Work = (Weight × Distance) × Cos(0°)
As the water is being pumped vertically upward, the distance is the height the water is lifted.
Now, we need to calculate the height the water is lifted.
The water leaves the engine with a velocity of 3 m/s vertically upward. And at the highest point, the velocity reduces to 0 m/s. Using the formula for velocity in free fall:
v² = u² + 2as
Where v = final velocity (0 m/s), u = initial velocity (3 m/s), a = acceleration due to gravity (-9.8 m/s²), and s = vertical distance covered.
Plugging in the values and solving the equation, we can find the height (s) the water is lifted.
Once we have the height, we can calculate the work done using the formula mentioned above.
Finally, to find the power, we use the formula: Power = Work done / Time taken
Given that one round of pumping out the water takes 1 second, we can substitute the calculated work done and time in the power formula to get the power in watts.
To convert the power to kilowatts, we divide the power by 1000.
Following these steps, we can find the power of the engine in kilowatts.