- #1
Rachael Hardman
- 1
- 0
Hello,
My question is about using vector components to find a force in a particular direction.
I already have the answer, I just don't understand it and would like an explanation if anyone has one.
If I have two vectors with radial velocities (in this case it's measurements of ocean current speed and direction) of [itex] \nu_{R1} [/itex] and [itex] \nu_{R2} [/itex] whose directions, [itex] \theta_1 [/itex] and [itex] \theta_2 [/itex] respectively, correspond to the angle they make with the x-axis (anticlockwise i.e. 0 -> 360 degrees), how can I combine these to find the vector value in both the north and east directions (i.e. 90% and 0%)?
The answer I've found is:
[itex] u = \dfrac{\nu_{R1}\cos(\theta_2)-\nu_{R2}\cos(\theta_1)}{\sin(\theta_2-\theta_1)} \qquad v=\dfrac{\nu_{R2}\sin(\theta_1)-\nu_{R1}\sin(\theta_2)}{\sin(\theta_2-\theta_1)}, [/itex]
where [itex] u [/itex] and [itex] v [/itex] are the north and east components respectively.
I've checked this numerically and it works - a sound explanation would be great though!
Please let me know if any clarification is needed or any diagrams/etc are required.
Many thanks,
Rachael
My question is about using vector components to find a force in a particular direction.
I already have the answer, I just don't understand it and would like an explanation if anyone has one.
If I have two vectors with radial velocities (in this case it's measurements of ocean current speed and direction) of [itex] \nu_{R1} [/itex] and [itex] \nu_{R2} [/itex] whose directions, [itex] \theta_1 [/itex] and [itex] \theta_2 [/itex] respectively, correspond to the angle they make with the x-axis (anticlockwise i.e. 0 -> 360 degrees), how can I combine these to find the vector value in both the north and east directions (i.e. 90% and 0%)?
The answer I've found is:
[itex] u = \dfrac{\nu_{R1}\cos(\theta_2)-\nu_{R2}\cos(\theta_1)}{\sin(\theta_2-\theta_1)} \qquad v=\dfrac{\nu_{R2}\sin(\theta_1)-\nu_{R1}\sin(\theta_2)}{\sin(\theta_2-\theta_1)}, [/itex]
where [itex] u [/itex] and [itex] v [/itex] are the north and east components respectively.
I've checked this numerically and it works - a sound explanation would be great though!
Please let me know if any clarification is needed or any diagrams/etc are required.
Many thanks,
Rachael