To find the magnitude of the average force exerted on the water by the blade, we can use the principle of conservation of momentum.
The momentum of an object can be calculated by multiplying its mass by its velocity. Since the mass of water per second that strikes the blade is given as 33.6 kg/s, we can calculate the momentum before and after the interaction:
Momentum before = mass of water per second * velocity of incident water stream
= 33.6 kg/s * 17.4 m/s
Momentum after = mass of water per second * velocity of exiting water stream
= 33.6 kg/s * (-15.0 m/s)
According to the conservation of momentum, the momentum before the interaction must be equal to the momentum after the interaction:
Momentum before = Momentum after
33.6 kg/s * 17.4 m/s = 33.6 kg/s * (-15.0 m/s)
From this equation, we can solve for the mass of water per second:
33.6 kg/s * 17.4 m/s = 33.6 kg/s * (-15.0 m/s)
584.64 kg m/s = -504 kg m/s
Next, we can find the magnitude of the average force exerted on the water by using the formula:
Force = (Change in momentum) / (Time)
Since the mass of water per second is constant, the force can be calculated as:
Force = [(mass of water per second) * (change in velocity)] / (Time)
The change in velocity is the difference between the velocity of the incident water stream and the velocity of the exiting water stream:
Change in velocity = |velocity of incident water stream| - |velocity of exiting water stream|
= 17.4 m/s - (-15.0 m/s)
= 32.4 m/s
Finally, we can substitute the values into the formula to calculate the magnitude of the average force:
Force = [(33.6 kg/s) * (32.4 m/s)] / (Time)
Please provide the value for the time of interaction so that we can calculate the magnitude of the average force exerted on the water by the blade.