A car is traveling 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.
I can think of two possible vector expressions which should be equivalent. I am clearly doing something wrong because they are not.
vwg = velocity of wind wrt ground
vcg = velocity of car wrt ground
vwc = velocity of wind wrt car
vwg = vwc + vcg
Expression 2 (following the rule of subtracting the observer's movement)
Yes - I'm aware I should add the negative vector and that the negative sign means the reverse direction
The Attempt at a Solution
The solution vector diagram is (excuse the dots so I don't lose the spaces):
|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
The solution vector diagram is:
...\ ...| vwc
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?