When a fan pushes air backwards with a force of 150 N, as per Newton's Third Law of Motion, the air exerts an equal and opposite force on the boat. Therefore, the forward force of the air on the boat is also 150 N.
Calculating Acceleration of the Boat
To find how far the boat will travel in the first minute, we first need to calculate the acceleration of the boat. The acceleration (\(a\)) can be found using Newton's Second Law of Motion, which states that \(F = ma\).
Given:
- Force \(F = 150 , \text{N}\)
- Mass \(m = 220 , \text{kg}\)
We can rearrange the formula to find acceleration: \[ a = \frac{F}{m} = \frac{150 , \text{N}}{220 , \text{kg}} \approx 0.6818 , \text{m/s}^2 \]
Calculating Distance Travelled
Now, we can find the distance the boat travels in the first minute (60 seconds). For an object starting from rest with constant acceleration, the distance \(d\) can be calculated with the formula: \[ d = \frac{1}{2} a t^2 \]
Plugging in the values:
- \(a \approx 0.6818 , \text{m/s}^2\)
- \(t = 60 , \text{s}\)
Calculating the distance: \[ d = \frac{1}{2} \times 0.6818 , \text{m/s}^2 \times (60 , \text{s})^2 \] \[ d = 0.3409 , \text{m/s}^2 \times 3600 , \text{s}^2 \approx 1227.24 , \text{meters} \]
Changing Direction and Speed
The fan on the airboat can be utilized to change the direction and speed of the boat in the following ways:
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Changing Direction: The angle at which the fan is pointed can be adjusted. By tilting the fan to one side, the thrust will push the boat in a new direction, allowing for maneuverability. The boat can effectively turn by redirecting the air thrust instead of relying solely on the water flow.
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Increasing Speed: To increase the speed of the boat, the fan can be set to exert more force. This could be accomplished by increasing the power to the fan, making it more efficient at moving air backwards and thus generating a greater forward force on the boat.
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Decreasing Speed: Conversely, to decrease the speed, the fan can reduce its output force. This can be implemented either by throttling back the power to the fan or by adjusting the fan's angle so that less thrust is directed backwards, allowing drag forces to slow the boat down.
In summary, the fan provides thrust that directly correlates to the boat's motion, and its position and power can be adjusted for enhanced control over the boat's trajectory and velocity.
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