Solve 2D Motion Homework: Wind Gust Accelerates Boat East

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In summary, the problem involves a sailboat traveling east at 5.0m/s and experiencing an acceleration of 0.80m/s^2 at a direction of 40 degrees north of east. The question asks for the boat's speed 6 seconds later when the gust subsides. To solve this problem, the initial velocities in the x and y directions are known, as well as the time. The components of acceleration must be found and then combined to find the magnitude of the final velocity using the equation V = V0 + at.
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Homework Statement


A sailboat is traveling east at 5.0m/s. A sudden gust of wind gives the boat an acceleration a =(0.80m/s^2) (40 north of east).



Homework Equations


What is the boat's speed 6\;s later when the gust subsides?

I know the answer is 9.21m/s, but I am having difficulty breaking down the acceleration into its components. How would you start this problem and do I need to find Ax and Ay or am i going about this the wrong way.



The Attempt at a Solution



So far I have
Vx0= 5m/s
Vy0= 0m/s
t=6s
Ax=?
Ay=?
and Think the equation I need to use is Vx= Vx0+Axt then do the same for Y
and combine the two .
 
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Okay I figure it out i was doing it right but when it cam e to combining the two components i was just adding them instead of finding the magnitude for velocity. Which involve taking the sqaure root of the squares of the components.
 

Related to Solve 2D Motion Homework: Wind Gust Accelerates Boat East

1. How do you calculate the velocity of a boat being accelerated by a wind gust in the east direction?

The velocity of a boat can be calculated using the formula v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. In this case, the initial velocity would be the boat's current velocity, and the acceleration would be the force of the wind gust in the east direction. Simply plug in the values and solve for v.

2. What is the difference between acceleration and velocity?

Acceleration is the rate of change of velocity over time. It describes how much an object's velocity changes in a certain amount of time. Velocity, on the other hand, is the displacement of an object in a certain direction over time. In simpler terms, acceleration is how fast an object is speeding up or slowing down, while velocity is how fast an object is moving and in what direction.

3. How does the force of the wind gust affect the boat's acceleration?

According to Newton's second law of motion, force is directly proportional to acceleration. This means that the greater the force of the wind gust, the greater the acceleration of the boat will be in the east direction. However, the boat's mass also plays a role in the acceleration, as a heavier boat will require more force to accelerate compared to a lighter boat.

4. Can you solve for the time it takes for the boat to reach a certain velocity?

Yes, the time it takes for the boat to reach a certain velocity can be calculated using the formula t = (v - u) / a, where t is the time, v is the final velocity, u is the initial velocity, and a is the acceleration. Simply plug in the values and solve for t.

5. How do you take into account the boat's direction when calculating the acceleration?

When calculating the acceleration of the boat due to a wind gust, the direction of the boat must be taken into account. This can be done by using vector components and breaking down the acceleration into its horizontal and vertical components. In this case, the horizontal component would represent the acceleration in the east direction, while the vertical component would represent the acceleration in the north direction.

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