Edexcel M4 help please!
I'm not great at relative motion and i found this particular question reaaally hard so can anyone help me? (and this is a past exam question)
question: a boat is sailing north at a speed of 15km/h. To an observer on the boat the wind appears to blow from a direction of 30 degrees.
The boat turns around and sails due south at the same speed (-15km/h). The velocity of the wind relative to the Earth remains constant, but to an observer on the boat it appears to blow from 120 degrees.
Find the velocity of the wind relative to the earth
(answer: -1/2(15root3i +15j) )
question: a boat is sailing north at a speed of 15km/h. To an observer on the boat the wind appears to blow from a direction of 30 degrees.
The boat turns around and sails due south at the same speed (-15km/h). The velocity of the wind relative to the Earth remains constant, but to an observer on the boat it appears to blow from 120 degrees.
Find the velocity of the wind relative to the earth
(answer: -1/2(15root3i +15j) )
Original post by lanki_bones
(answer: -1/2(15root3i +15j) )
(answer: -1/2(15root3i +15j) )
I agree with the given answer.
To get you started.
We need a basic equation, so, if we let E=Earth,B=Boat, and W=Wind, then considering relative velocities, we have.
Where is the velocity of the wind relative to the Earth, etc.
Since we only know the direction of the wind relative to the boat, then the velocity of the wind relative to the boat is going to be some scalar multiple of a direction vector.
Also, note that the direction the wind is coming from is 180 degrees to the direction the wind is blowing in.
There's enough information there to get started, and create two equations, one for each scenario of the boat's velocity. And solve.
Note that the scalar multiple will be different in each equation.
Have a go, and see what you can do.
(edited 11 years ago)
thak you so much however i'm a little bit confused about your comment on the direction of the wind.
As stated in the quesiton, the observer initially sees the wind blowing from 30 degrees so does that mean the wind is blowing in at 210 degrees or 150 degrees ?
Original post by ghostwalker
Also, note that the direction the wind is coming from is 180 degrees to the direction the wind is blowing in.
Also, note that the direction the wind is coming from is 180 degrees to the direction the wind is blowing in.
As stated in the quesiton, the observer initially sees the wind blowing from 30 degrees so does that mean the wind is blowing in at 210 degrees or 150 degrees ?
Original post by lanki_bones
As stated in the quesiton, the observer initially sees the wind blowing from 30 degrees so does that mean the wind is blowing in at 210 degrees or 150 degrees ?
As stated in the quesiton, the observer initially sees the wind blowing from 30 degrees so does that mean the wind is blowing in at 210 degrees or 150 degrees ?
Just to clarify.
If the wind is blowing from the North, it is going South. And if it is coming from the East, it is going West, etc.
So, add, or subtract 180, as appropriate to keep in the range 0 to 360.
finally got round to doing the question and I still keep getting the wrong answer and I'm not too sure what i'm doing wrong
let A be the boat , W the wind
so for initial direction : wVa= Vw-Va
so xsin30i+xcos30j= xi+xj-15i
then i set up a similar equation for the boat travelling south using 60 degrees as my angle and try to solve for Vw
hope you can help thanks
let A be the boat , W the wind
so for initial direction : wVa= Vw-Va
so xsin30i+xcos30j= xi+xj-15i
then i set up a similar equation for the boat travelling south using 60 degrees as my angle and try to solve for Vw
hope you can help thanks
Original post by lanki_bones
finally got round to doing the question and I still keep getting the wrong answer and I'm not too sure what i'm doing wrong
let A be the boat , W the wind
so for initial direction : wVa= Vw-Va
so xsin30i+xcos30j= xi+xj-15i
then i set up a similar equation for the boat travelling south using 60 degrees as my angle and try to solve for Vw
hope you can help thanks
let A be the boat , W the wind
so for initial direction : wVa= Vw-Va
so xsin30i+xcos30j= xi+xj-15i
then i set up a similar equation for the boat travelling south using 60 degrees as my angle and try to solve for Vw
hope you can help thanks
Vw is not going to involve x.
Let Vw= ai+bj say, if you've going to break it down, though there is no need to do so. I'd just leave it as Vw
It's easiest if you leave your equations in the form Vw=....
Then you can equate the two and solve that way
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