Motion in a Plane Flashcards
Prove Parallelogram law of vector addition
If two vectors can be represented both in magnitude and direction by the adjacent sides of a parallogram drawn from a common point, then their resultant is completely represented, both in magnitude and direction, by the diagonal of the parallelogram drawn from that point
Magnitude of resultant R and direction + proof
R = root (A^2 + B^2 + 2AB cos theta)
tan beta = B sin theta / (A + B cos theta)
Unit vector formula
(Ax i + Ay j + Az k) / root (Ax^2 + Ay^2 + Az^2)
Scalar Product
A . B = AB cos theta
Vector Product (area parallelogram)
A x B = AB sin theta
Condition for perpendicular vectors
Scalar product is zero
Condition for parallel vectors
Vector product is zero
Projection of vector A on B
(A . B)/ (|B| mag) * B vector
Unit vector n perpendicular to plane of vectors A and B
n^ = A x B / mag |A x B|
Projectile Derivations
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Projectile imp formulas
tm = u sin theta / g
t(f) = 2u sin theta / g
h(m) = u^2 sin^2 theta / 2g
R = u^2 sin 2theta / g
y = x tan theta - gx^2 / (2u^2 cos^2 theta)
Max horizontal range when
theta = 45 degrees
Rm = u^2 / g
When is horizontal range the same
(45 + theta) & (45 - theta)
Max horizontal range and max height
Hm = Rm / 4 = u^2 / 4g
Angular displacement
theta = s / r
