A ship sails 40 km[N30°E], then 50km[E], then 70km[N60°W], then 60km[N45°W], then 100km[S], then 150km[W], and finally 80km[S20°W]. Determine: a) The resultant Velocity if the trip took 25 hours. b) Calculate the distance and average speed.
READ THIS before you start doing it this is just to get you an idea on what I am expecting :
When adding several vectors together, we could add the first two, solve for the resultant using the sine and cosine laws. Then add the third vector to that resultant, to get a new resultant. Then add the fourth vector to that resultant to get another new resultant. Repeating the procedure until we arrived at the final resultant. Solving this series of triangles would be very tedious and time consuming.
The better way is of course by breaking each of the original vectors into components, and finding the total [N-S] component, and the total [E-W] component. Then add these two vectors tip-to-tail to get the final resultant. Since the vectors are at right angles, you would use the pythagorean theorem to determine the final length, and SOHCAHTOA to find the direction.
To do this problem: sketch each of the vectors from the origin on the cartesian plane. Decide whether you will measure all angles(in a counterclockwise direction) from the East Cardinal Direction (X axis) - If you choose this method, positive horizontal results will be [E], while negative will be [W], and positive vertical results will be [N] and negative will be [S] - OR - measure all angles from the {E-W] axis, with all angles being between0° and 90°. Should you choose this second method, all answers will be positive, so you must determine whether the vertical component is [N] or [S], and whether the horizontal component is [E] or [W].
The nice thing about measureing angles from the East axis is that you just total the components, being careful of the signs on the numbers. If you choose to measure all angles from the E or W axis, making all angles between 0° and 90°, you have to record which vectors are East and which are West, and take that into account when totalling up the components. It is not difficult, just one thing to keep an eye on.
Give it a try, and submit when you are content with your answer. I will be looking at the calculations, so show your work. In the chart it is a good idea to show the substitution in for d and Θ, and then show the answer. Carry a couple of decimal places to avoid rounding errors.
![Vector Component Problem
A ship sails 40 km[N30°E], then 50km[E], then 70km[N60°W],
then 60km[N45°W], then 100km [S], then 150km[W], and finally
80km[S20°W].
Determine:
a) The resultant Velocity if the trip took 25 hours.
b) Calculate the distance and average speed.
Vector | dx = d cose dy = d sine
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