Solve 2D Motion Homework: Wind Gust Accelerates Boat East

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SUMMARY

The discussion centers on solving a 2D motion problem involving a sailboat experiencing an acceleration due to wind. The boat initially travels east at 5.0 m/s and receives an acceleration of 0.80 m/s² at an angle of 40 degrees north of east. After 6 seconds, the final speed of the boat is calculated to be 9.21 m/s. The key to solving this problem lies in correctly breaking down the acceleration into its x and y components and using the appropriate kinematic equations to find the resultant velocity.

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  • Familiarity with kinematic equations
  • Knowledge of trigonometric functions for angle calculations
  • Ability to calculate vector magnitudes from components
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  • Practice breaking down vectors into components using trigonometric functions
  • Learn to apply kinematic equations in two dimensions
  • Explore the concept of vector addition and resultant velocity calculations
  • Study examples of motion problems involving acceleration at angles
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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.
 

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