Solving Vector Coordinates Problem for Circular Movement

[brad sue]

hi ,
I have a problem about vector coordinates. this is the problem.

We have a 2-dimension space [x(unit vector i) and y( unit vector j)].

I have a circle of center 0 (0,0) and a point P such that OP = r.

Vector OP and the x-axis have an angle of θ .

there is a unit vector i_r , with the same direction with OP( but starting at P.)

Another unit vector i_t starts at P , but i_t is perpendicular to vector i_r. ( i_t 's direction is toward north-west)

Express vector i_r as a combination of unit vectors i and j.

Express vector i_t as a combination of unit vectors i and j.

I found that i_r = cos(θ ) i + sin(θ ) j

how to find i_t ? when I try to compute for i_t, I found the same as i_r, but I am not sure.

Please help

Thank you

 

[Doc Al]

Since i_t is perpendicular to i_r, they cannot have the same components. Draw a careful diagram. (I suspect you are mixing up your sines and cosines.)

 

[brad sue]

Since i_t is perpendicular to i_r, they cannot have the same components. Draw a careful diagram. (I suspect you are mixing up your sines and cosines.)

OK, I follow your suggestion and now I find:

i_t= sin(θ )i +cos(θ ) j

I do not know if you did the problem but I believe it is ok now

 

[Doc Al]

It's almost right. To see what's wrong, test if these vectors are perpendicular.

 

[brad sue]

Since i_t is perpendicular to i_r, they cannot have the same components. Draw a careful diagram. (I suspect you are mixing up your sines and cosines.)

Doc please I need help for this problem. Someone reply me but I need more information to complete it. It is urgent !

This is a problem I have . But because I cannot include the graph, I try to do via Microsoft Word. I put it as an attachment. I hope that you will understand it.

This is the problem:

Traffic signals are placed along a straight road at positions x = 0 m, x = 600 m, and x = 1200 m (see graph in attachment)). The time intervals during which the signals are green are shown by the thick lines ( in red) in the figure.

(a) Draw the displacement-versus-time curves (fastest and slowest) for a car that passes through all the lights when the car moves with constant speed.

(b) Draw a similar set of lines for a car traveling in the opposite direction.

(c) Assuming that the lights are timed such that a car passes through all lights in the middle of the time interval, what is the speed for which the lights are timed?

(d) What is the fastest constant speed of a car that makes it through all the signals, assuming it arrives at the first light at the optimal moment?

For info.:
The grah is a 2 dimension space with time(s) on horizontal and the position x(m) in vertical.
The interval are put in red and I mentioned the time interval at the end of each line.Please help me with that . I do not understand it

Thank you very much.

Brad

 

[HallsofIvy]

Did you read Doc Al's last post:
"It's almost right. To see what's wrong, test if these vectors are perpendicular."

You had said " ir = cos(θ ) i + sin(θ ) j" and "it= sin(θ)i+ cos(θ)j"

Remember that the dot product of two perpendicular vectors is 0. Here the dot product would be cos(θ)sin(θ)+sin(θ)cos(θ).
Do you see what is wrong? Now look at your picture again.

 

[brad sue]

Did you read Doc Al's last post:
"It's almost right. To see what's wrong, test if these vectors are perpendicular."

You had said " ir = cos(θ ) i + sin(θ ) j" and "it= sin(θ)i+ cos(θ)j"

Remember that the dot product of two perpendicular vectors is 0. Here the dot product would be cos(θ)sin(θ)+sin(θ)cos(θ).
Do you see what is wrong? Now look at your picture again.

I got it
it =-sin(θ)i+ cos(θ)j

Hallsofivy,
Please can take a look at the problem ( about the car and the 3 lights) just above this quote. I do not know if Doc will be available today.

Please give some suggestions.


Thanks