To find the magnitude of the average force exerted on the water by the blade, we can use the conservation of linear momentum.
The formula for linear momentum is given by:
Momentum = mass × velocity
Initially, the momentum of the incoming water stream is given by:
Initial Momentum = mass × initial velocity
Similarly, the momentum of the exiting water stream is given by:
Final Momentum = mass × final velocity
According to the conservation of linear momentum:
Initial Momentum = Final Momentum
Therefore, we can write the following equation:
mass × initial velocity = mass × final velocity
Simplifying the equation, we get:
mass × (initial velocity - final velocity) = 0
Now, we can substitute the given values into the equation:
33.6 kg/s × (17.4 m/s - (-15.0 m/s)) = 0
Calculating this equation, we have:
33.6 kg/s × (32.4 m/s) = 1088.64 kg·m/s
This value represents the change in momentum per second of the water stream.
Since force is defined as the rate of change of momentum, we can calculate the force exerted on the water by dividing the change in momentum by the time interval taken to produce that change.
However, the time interval is not given in the question. Therefore, we cannot determine the magnitude of the average force exerted on the water by the blade without the time interval.