A sailboat traveling east

1. Jan 31, 2015

iSimply

1. The problem statement, all variables and given/known data
A sailboat is traveling due east, with a speed V=Vinit at time t = 0 and a constant eastward acceleration A(motor). From a time t = t(gust) to a time t=t(calm), a gust of wind gives the boat an additional acceleration A(wind) at an angle 60o North of East. Find an expression in terms of the quantities given for the North and East components of the boat's velocity at the time t(calm).

2. Relevant equations
Just basic 2 dimensional kinematic like
Vfs= Vis + Ast
Sf= Si+ Vis(t) + 1/2 As(t)^2

3. The attempt at a solution

I thought about this and think East components = Vinit + ( A motor + A wind (1/2)) (tcalm-t0)
and North components = A wind (√3/2) (tcalm-t0)

I mostly added the vectors of A wind and A motor, I am not sure if that is right. Please clarify or correct me if I am wrong, thank you.

2. Jan 31, 2015

Nathanael

Why from t0 to t(calm)? Is that the correct time period in which the wind is blowing?

Again, is that the time that the wind acts?

3. Jan 31, 2015

iSimply

I wasn't sure if from t0 to Tgust there was a time difference.
If the point where Tgust happens then it would only be from Tcalm-Tgust.
Is the rest of it correct?

4. Feb 1, 2015

Nathanael

If they say it starts at tgust then you shouldn't assume tgust=t0

The rest is correct, but write out the equation for the East component so I can see that you do it correctly.

5. Feb 1, 2015

iSimply

Well for the East component we have a Vinit and 2 acceleration component acting on it. Which are Amotor and Awind.
And we know that Awind is 60 degree north east so the Awind in the east direction would be equal to Awindcos60degree

So Velocity for the East component is equal to Vinit+ (Amotor + Awind cos 60) (tgust-tcalm).
Does it look correct?

6. Feb 1, 2015

Nathanael

Did we only turn on the motor on once the wind starting blowing?

7. Feb 1, 2015

iSimply

No... :(
That was the part where I was confused and wasn't sure how to approach it.
I know that from t0 to tgust the motor was running, but I wasn't sure how to incorporate it.

V east= Vinit + (motor (t0-tgust))+ (motor + wind)(tcalm-tgust)...

8. Feb 1, 2015

Nathanael

Write it in pieces. What is the velocity once the wind starts blowing? Then what is the velocity after the wind stops blowing?

Also I just noticed one more small error. You wrote (tgust - tcalm), does anything seem wrong with that?

9. Feb 1, 2015

iSimply

Yeah it should be (tcalm - tgust) good catch.
Well it goes from Vinit+ (motor(tgust-t0)) when the wind start.
Then once it stop then wouldn't it be that plus ( motor + windcos 60)(tcalm-tgust).

so it would be Vinit + (motor (tgust-t0))+ (motor +windcos 60)(t calm-tgust).
Is that right?

10. Feb 1, 2015

Nathanael

Yep :) (You can simplify it slightly because t0=0)

11. Feb 1, 2015

iSimply

Oh and an edit my to North Component it should be = A wind (√3/2) (tcalm-tgust)
since no north component was acting it on from t0 until tgust.

You are awesome, thank you for the help!

12. Feb 1, 2015

Nathanael

Indeed

You're welcome