Calculating Speed and Direction of Sailboat After Gust of Wind

This approach is probably easier.In summary, when a sailboat traveling east at 5m/s experiences a gust of wind with an acceleration of 0.80 m/s^2 at a 40 degree angle north of east, its speed 6 seconds later is approximately 7.6 m/s and its direction is approximately 44 degrees north of east.
  • #1
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A sailboat is traveling east at 5m/s . A sudden gust of wind gives the boat an acceleration=.80 m/s^2, (40 degrees north of east).

A. What is the boat's speed 6 seconds later when the gust subsides?
________m/s

B. What is the boat's direction 6 seconds later when the gust subsides?
________degrees north of east.


My attempts:
v = v0 + at
v = (0) + (0.80m/s^2)* (6sec)
v = 4.8m/s

A^2+ B^2 = C^2
(4.8)^2 + (5.0)^2 = 48.04
C= 6.9 m/s
_____________________

tan-1 (4.8/5.0) = 44°


Please tell me what I did wrong? I am so stuck :(
 
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  • #2
Kster said:
A^2+ B^2 = C^2
(4.8)^2 + (5.0)^2 = 48.04
C= 6.9 m/s
This assumes that the acceleration is perpendicular to the original velocity (east). But it's not: the acceleration is 40 degrees north of east.

Hint: Break the acceleration (and the velocity) into components (east and north). Find the final velocity component east and the final velocity component north, then you can combine them to find the final speed.

Another approach is to find the change in velocity along the direction of the acceleration, which will be some vector 40 degrees north of east. Then just add that vector to the initial velocity vector and find the new magnitude.
 
  • #3


Firstly, for part A, you have correctly calculated the boat's speed after 6 seconds. However, you have not answered the question, which asks for the boat's speed when the gust subsides. This means that you need to add the initial speed of 5m/s to the final speed of 4.8m/s to get the total speed when the gust subsides.

Therefore, the boat's speed 6 seconds later when the gust subsides is 9.8m/s.

For part B, you have used the Pythagorean theorem to calculate the hypotenuse (C) of the triangle formed by the initial velocity and the acceleration due to the gust. However, this does not give you the direction of the boat. To find the direction, you can use trigonometric functions.

Firstly, we need to find the angle (θ) between the initial velocity and the final velocity. To do this, we can use the dot product formula:

v1 · v2 = |v1| * |v2| * cosθ

where v1 and v2 are the initial and final velocities, respectively.

We know that the initial velocity is 5m/s and the final velocity is 4.8m/s. So, the dot product becomes:

(5)(4.8) = (5)(4.8) * cosθ

cosθ = (5)(4.8) / (5)(4.8)

cosθ = 1

θ = cos^-1(1)

θ = 0°

This means that the angle between the initial and final velocity is 0°, which also happens to be the angle between the initial velocity and the direction of the gust (40° north of east).

To find the boat's direction, we need to add 40° to the initial direction of east. Therefore, the boat's direction 6 seconds later when the gust subsides is 40° north of east.

I hope this helps! Let me know if you have any further questions.
 

1. What factors affect the speed and direction of a sailboat after a gust of wind?

Several factors can affect the speed and direction of a sailboat after a gust of wind. These include the strength and direction of the gust, the design and size of the sailboat, the shape and size of the sails, the position and angle of the sails, and the weight distribution on the boat.

2. How do you calculate the speed of a sailboat after a gust of wind?

The speed of a sailboat after a gust of wind can be calculated using the formula: Speed = Wind Speed x Sin(Angle of Sails). This formula takes into account the strength and direction of the gust, as well as the angle of the sails in relation to the wind.

3. Can the direction of a sailboat after a gust of wind be controlled?

Yes, the direction of a sailboat after a gust of wind can be controlled by adjusting the position and angle of the sails. By changing the angle of the sails, the boat can be steered in a different direction, allowing for greater control and stability.

4. How does the size and shape of the sails affect the speed and direction of a sailboat after a gust of wind?

The size and shape of the sails play a crucial role in determining the speed and direction of a sailboat after a gust of wind. Larger and more curved sails can catch more wind, resulting in a higher speed. The shape of the sails also affects the aerodynamics of the boat, which can impact its direction.

5. What are the safety precautions to consider when calculating the speed and direction of a sailboat after a gust of wind?

When calculating the speed and direction of a sailboat after a gust of wind, it is important to consider the safety precautions. These include wearing appropriate safety gear, having a knowledgeable and experienced captain, checking weather conditions before sailing, and being aware of potential hazards on the water.

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