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a quantity that has magnitude but no direction
a physical quantity that has both direction and magnitude.
the sum of two or more vectors.
To add vectors graphically
1. place tail of second vector at head of first vector keeping its direction the same.
2. draw resultant vector from the tail of the first vector to the head of the second.
Analytical components of vector addition:
1. To add perpendicular vectors use
a. Pythagorean formula
b. soh cah toa
: a vector can be resolved into its components (vector resolution).
2. To add vectors that are not
a. resolve vectors into its components
b. add all vertical components
c. add all horizontal components
d. find the resultant (see #1 above)
Use the law of cosines and sines.
horizontal and vertical motions of a projectile
The horizontal and vertical motions of a projectile are independent of one another, in the absence of air resistance.
is the curved path that an object follows when thrown, launched, or otherwise projected near the surface of Earth.
the objects thrown.
constant acceleration in the vertical direction
With constant acceleration in the vertical direction use accelerated motion formulas.
constant velocity in horizontal direction
With constant velocity in horizontal direction
v = x/t; xh = vht
Objects projected at an angle:
1. resolve vector into vh and vv.
*Use only these components to solve the problem; never again use the original vector!
2. for vertical motion use:
vvf = vvi + gt to get time for half of the trajectory.
xv = ½ gt2 to get vertical height.
3. for horizontal motion (range):
xx = vxttotal (use double of t).
Note: *rising time = falling time
*horizontal distance moved in each half of trajectory are equal.
* 45o angle of launch gives maximum range.
velocity measurements depend on the frame of reference of the observer.
Physics: Two Dimensional Motion and Vectors