Vector expressions - equivalence

  • Thread starter jemerlia
  • Start date
  • #1
28
0

Homework Statement


A car is travelling at 12ms^-1. To the passenger in the car the wind appears to be blowing at 8.0ms^-1 at right angles to the road. What is the magnitude and direction of the velocity of the wind with respect to the ground.


Homework Equations


I can think of two possible vector expressions which should be equivalent. I am clearly doing something wrong because they are not.
Using:
vwg = velocity of wind wrt ground
vcg = velocity of car wrt ground
vwc = velocity of wind wrt car
Expression 1
vwg = vwc + vcg

Expression 2 (following the rule of subtracting the observer's movement)
vwc= vwg-vcg

Yes - I'm aware I should add the negative vector and that the negative sign means the reverse direction

The Attempt at a Solution



Expression 1:
The solution vector diagram is (excuse the dots so I don't lose the spaces):

^----------->vcg
|..............^
|vwc ..... /
|........ / vwg
|....../
|../
|/
It gives a vwg magnitude of c. 14ms^-1 and a direction of tan^-1(8/12) = c. 34 degrees with the wind coming from behind the car

Expression 2:
The solution vector diagram is:

<----------------- -vcg
.^.......................^
....\....................|
........\ ...............| vwc
....vwg..\.............|
..............\..........|
..................\......|
......................\..|
.........................\|
Of course the magnitude is the same as in the previous example but the direction is
tan^-1 (8/-12) = -34 degrees.

My concern is that the wind appears to be coming from the front!

Gloom - what have I misunderstood?

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
Your method is correct. The answer is not exactly 14m/s. In both cases it is only the direction you start with that results in the -ive or +ive sign. Why do you think the wind appears to be coming from the front?
 
  • #3
28
0
Thank you for your reassurance. I lacked the confidence to be certain the second vector diagram was the equivalent of the first - especially because vector arithmetic is new to me. I would like to ask this naive question - if a, b and c are vector quantities and they are related:
a = b+c
then is it correct to transpose so that:
b= a-c
?

Why did I think the wind was coming from the front? The honest answer is twofold: first: sometimes I have a pathological inability to imagine the behaviour of the real word and, second I had convinced myself the second expression/vector diagram was telling a different story to the first.
 

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