Activity 2: Vector components in a coordinate system. The actual physical direct

Question

Activity 2: Vector components in a coordinate system. The actual physical direction of , is geographical North- Thornton is parallel to19" Ave, which runs North-South. Thus gives the direction of a North coordinate axis. Con an East axis at right angles to North, and project each of the vectors and , onto these axes to find East and North components for each. Make a table giving for each of the three vectors magnitude, direction clockwise from North (navigation convention), and the North and East components. Construct on of a North coordinate axis. Verify the component addition rule: the sum of the north components of V and equal

Explanation / Answer

V1 = 0.75 m this is in north direction
I am representing north direction by +Y axis and East direction by +X axis
So vecctor 1 is in the +Y direction
Now Vector 2 is 30 degree clock wise from north or from + Y axis
V2 = 0.5 m
Vector 3 is 11.9 degree clock from north or +Y axis
Now I will break these into its components
First vector 2
Since it is making 30 degree angle with +Y or north axis therefore its component along +Y direction
= V2Cos30 = 0.5*Cos30 = 0.433 m
Its component along +X axis or east axis
= V2Sin30 = 0.25 m
Now vector 3 is making angle 11.9 degree from north therefore
along Y axis = V3Cos11.9 = 1.21Cos11.9 = 1.184 m
along X axis = V3Sin11.9 = 0.2495 m

Now we add all componet along X axis = 0.2495 + 0.25 = 0.4995 m
Y componet = 1.184 + 0.433 + 0.75 = 2.367 m
Now net resultant = (X2 +Y2)1/2 = 2.419 m
Direction = tan-1(Y/X)
Angle = 11.916 degree anticlockwise direction from +X axis or East axis

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