How Do You Calculate the Average Acceleration of a Sailboat Changing Direction?

[chroncile]

Homework Statement

If a sailboat is heading East at 18 m/s and it makes a turn until it is heading 50^oNof E at 16 m/s, and the turn takes 2.5 minutes, what is the average acceleration of the boat in m/s²

Homework Equations

None

The Attempt at a Solution

I drew the vectors of 16 m/s N and 18 m/s E. What do I do next?

 

[PhanthomJay]

There is a relevant equation...what is the definition of average acceleration?

 

[chroncile]

I think it's


a_av = v / t

 

[PhanthomJay]

That's not right. Do you have a textbook or can you look it up online?

 

[rwisz]

To solve this problem, you can use the formula for average acceleration: a = (vf - vi)/t, where vf is the final velocity, vi is the initial velocity, and t is the time.

First, you need to find the final velocity (vf) of the boat. Since the boat is now heading 50 degrees north of east, you can use trigonometry to find the horizontal and vertical components of the final velocity. The horizontal component can be found using cos(50) = vf/16, which gives a horizontal component of vf = 12.26 m/s. The vertical component can be found using sin(50) = vf/16, which gives a vertical component of vf = 10.29 m/s.

Next, you can use the Pythagorean theorem to find the magnitude of the final velocity (vf). vf = √(12.26^2 + 10.29^2) = 15.81 m/s.

Now, you can plug in the values for vf, vi, and t into the formula for average acceleration: a = (15.81 m/s - 18 m/s)/2.5 min. Since the time is given in minutes, you need to convert it to seconds by multiplying it by 60. This gives a time of 150 seconds.

Plugging in the values, you get a = (-2.19 m/s)/150 s = -0.0146 m/s^2.

Therefore, the average acceleration of the boat during the turn is -0.0146 m/s^2. This indicates that the boat is slowing down during the turn.

It is also important to note that the direction of acceleration is towards the center of the turn, which is towards the north since the boat is turning towards the north. This means that the boat is accelerating towards the north during the turn.