- #1

- 25

- 0

**Sailboat problem-- components of acceleration**

1. Homework Statement [/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)

## Homework Equations

v(t)=v

_{0}+a*t

## The Attempt at a Solution

I divided the acceleration into its components, so a

_{x}= 0.8cos33 and a

_{y}= 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, v

_{y}=a

_{y}*t = 2.396 m/s.

I then used this to find the x and y position of the sailboat,

x= v

_{x}*t= 5.7 *5.5= 31.351 m east

y= v

_{y}*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: