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Equations_you_must_know_for_Exam_1.Fall_2011.

# Equations_you_must_know_for_Exam_1.Fall_2011. - α = β sin...

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Equations you must know for Exam 1 Fall 2011 Oct.06.2011. 1. Equations for kinematics handed out earlier ( 29 ( 29 ( 29 ( 29 ( 29 2 2 2 2 2 2 cos sin 1 1 ( ) ( ) ( ) 2 2 ( ) ( ) 2 ( ) 2 ( ) i i x i y i i i f i x f i x f i f i y f i y f i f i f i x x x f i y y y f i f i f i x x x f i y y y f i v v v v x x v t t a t t y y v t t a t t v v a t t v v a t t v v a x x v v a y y θ θ = = = + - + - = + - + - = + - = + - = + - = + - i i i x i y i 2. Decomposition of a projectile's initial velocity vector v into v v cos , v v sin and note the direction of the gravitational acceleration. θ θ = = r θ i v r i x v x Y g r i y v cos sin i x i i y i v v v v θ θ = = r r 3. Projectile motion for any given: 1

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( , ) ( sin , cos ) i i i x y i i v v v v v θ θ = = r 2 2 2 , , height, range sin 0 2 2 sin 0 ( ) 2 2 2 sin 2 cos sin cos sin 2 where we used 2sin co tof up total time of flight i y f i i i y y f y up up i y f i i i y y tof i i i i x tof i t t t H R v v v v gt v gt t g g v v gt gt y v t t v t g g v v v R v t v g g g θ θ θ θ θ θ θ θ = = = = - = - = = = - = - = = = = = = ( 29 ( 29 ( 29 ( 29 1 2 1 2 1 2 2 2 2 2 2 s sin 2 (See Part 4. Trig. Iden.) For a given and there are two solutions for theta: , and are complementary angles: 90 sin 2 2 2 2 i i i i i y y y y i y up up R v v v v v g H v t t g g g g θ θ θ θ θ θ θ θ θ = + = ° = - = - = = x y R H 2
4. Trigonometric Identities: sin ( α ± β ) = sin α cos β ± cos α sin β If α = β sin 2
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Unformatted text preview: α = β sin 2 α = 2sin α cos α 5. The Taylor Expansion for small angles sin θ up to first order in θ cos θ up to the second order in θ sin θ ; 2 cos 1 2-; Conversion of angle to radian: 1 17.5 180 radian millirad π ° = = ° 6. Relative velocity and the vector addition of velocities: a.) w.r.t. the observer affixed to the ground (shore) b b w s w s v v v = + r r r b.) w.r.t. the observer “o1” who is affixed to the moving object m1 while the informations for the two moving objects are given in ground based coordinate system: 1 2 , m m G G v v r r 2 2 1 1 m m m o G G v v v =-r r r 3...
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Equations_you_must_know_for_Exam_1.Fall_2011. - α = β sin...

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