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The force required to row a boat at constant velocity is proportional to the speed . If a speed of 4kmph requires 7.5kW how much power does a speed of 12 kmph require?
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The force required to row a boat at constant velocity is proportional ...
Understanding the Relationship Between Force and Power
The force required to row a boat at constant velocity is directly proportional to the speed of the boat. This means that if the speed increases, the force—and thus the power required—will also increase.
Given Data
- Speed 1 (V1) = 4 km/h
- Power 1 (P1) = 7.5 kW
- Speed 2 (V2) = 12 km/h
Proportionality Concept
Since the force (and therefore power) is proportional to speed, we can express this relationship as:
P ∝ V
This can be written in terms of a constant k:
P = k * V
Calculating the Constant
Using the first set of data:
7.5 kW = k * 4 km/h
To find k:
k = 7.5 kW / 4 km/h = 1.875 kW per km/h
Calculating Power at 12 km/h
Now, applying this constant to determine the power at a speed of 12 km/h:
P2 = k * V2
P2 = 1.875 kW per km/h * 12 km/h
P2 = 22.5 kW
Conclusion
Therefore, the power required to row the boat at a speed of 12 km/h is 22.5 kW. This illustrates how power demands increase with speed due to the proportional relationship between force and velocity.
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The force required to row a boat at constant velocity is proportional to the speed . If a speed of 4kmph requires 7.5kW how much power does a speed of 12 kmph require?
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