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Unformatted text preview: ds 2 = 2 + 2 + 2 ds 2 = 2 + 2 + 2 + 2 c = 299  79  2458 1 ds 2 = 2 + 2 Minkowski Special Relativity: 1908 Sep 21 ds 2 = + ( 29 ( 29 + ( 29 ( 29 + ( 29 ( 29 + ( 29 ( 29 dX = dY = dZ = ds 2 = + ( 29 ( 29 + ( 29 ( 29 + ( 29 ( 29 + ( 29 ( 29 ds 2 =  2 2 2 + 2 2 ds 2 =  2 2 2 + 2 ds 2 = 2 + 2 + 2 2 2 Chapter 3, #12 6 CLICKER QUESTIONS For the vectors and a = 3.0 ( 29 + 4.0 ( 29 b = 5.0 ( 29 +2.0 ( 29 1) give a + b in unitvector notation 2) give a + b as a magnitude 3) give a + b as a direction relative to i 4) give b a in unitvector notation 5) give b a as a magnitude 6) give b a as a direction relative to i ion in Two and Three Dimensions Motion in Two and Three Dimensions x y z r r 1 r r 2 r ur u ion in Two and Three Dimensions Displacement Vector r x y z r r 1 r r 2 r ur u r r 2 = 1 + r ur u = r r 2 r r 1 = x 2 i + y 2 j + z 2 k ( ) x 1 i + y 1 j + z 1 k ( ) = x 2 x 2 ( ) i + y 2 y 2 ( ) j + z 2 z 2 ( ) k r ur u = D x i + D y j + D z k ion in Two and Three Dimensions Average velocity & Instantaneous velocity r v avg = = + + = + + x y r r r v = ion in Two and Three Dimensions Average acceleration & Instantaneous acceleration r a = r a avg = = 2 1 r a = = + + ( 29 = + + a x = , = , = , To find the scalar components of a , differentiate the scalar components of v ion in Two and Three Dimensions Chapter 4, #19 The acceleration of a particle moving only on a horizontal x , y plane is given by where a is in m/s/s and time t is in seconds. r = 20.0 ( 29 + 40.0 ( 29 At t = 0, the position vector locates the particle, which then has the velocity vector v = 5.0 / ( 29 + 2.0 / ( 29 At t = 4.00 s, what are a) its position vector in unit vector notation b) the angle between its direction of travel and the positive direction of the x axis? The motions in x , and y , are independent! a = 3 + 4 a = 3 + 4 a = 3 + 4 THIS IS NOT A CONSTANT ACCELERATION PROBLEM! d 2 x d t 2 = 3 d 2 y d t 2 = 4 dy d t = 4 2 2 + 2 = 34 dx d t = 3 2 2 + 5 = 29 x = 3 2 3 3 + 5+ 20 = 72 y = 4 2 3 3 + 2+ 40 = 90.67 r = 72.0 ( 29 + 90.67 ( 29 ion in Two and Three Dimensions Chapter 4, #19 b) the angle between its direction of travel and the positive direction of the x axis?...
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 Spring '08
 bennet
 Physics

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