1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Sailboat problem- components of acceleration

  1. Feb 6, 2012 #1
    Sailboat problem-- components of acceleration

    1. The problem statement, all variables and given/known data[/b]
    A sailboat is travelling east at 5.70 m/s. A sudden gust of wind gives the boat an acceleration a=(0.800 m/s2,33.0° north of east). What is the boat's speed 5.50 s later when the gust subsides?
    What is the boats new direction? as an angle (degrees north of east)

    2. Relevant equations

    3. The attempt at a solution
    I divided the acceleration into its components, so ax= 0.8cos33 and ay= 0.8sin33 to give me the resultant acceleration to plug into the above formula. v(t)= 5.7 +(0.8cos33+0.8sin33)5.5 = 11.79 m/s, which is the wrong answer, but I'm not sure what I'm missing.
    For the second question (what's its new direction), I used the y-component of the acceleration (0.8sin33) to find the the y component of velocity. So, vy=ay*t = 2.396 m/s.
    I then used this to find the x and y position of the sailboat,
    x= vx*t= 5.7 *5.5= 31.351 m east
    y= vy*t= 2.396 * 5.5 = 13.18 north
    I then used the tan-1 function to find the angle. So, tan-1 13.18/31.351 = 22.8 degrees north of east, which is also wrong.
    Help please!
    Last edited: Feb 6, 2012
  2. jcsd
  3. Feb 6, 2012 #2
    Re: Sailboat problem-- components of acceleration

    For the first part you can't simply add the velocitys because they are vectors. what to need to do is find the size of the resultant vector:

    Vx=v(0)+v(x)*t Vy=v(y)*t

    Use Pythagoras to get the size of the resultant:


    For the second part you want the direction of travel so the angle you want is the angle of the resultant velocity:

  4. Feb 6, 2012 #3
    Re: Sailboat problem-- components of acceleration

    Got it, thanks!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook