Formula Sheet

Formula Sheet - VECTORS COLLISIONS Ballistic pendulum:...

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VECTORS A – B = A + (-B) = Acosθ = Asinθ A = √(A x ² + A y ² + A z ²) θ = tan -1 (A y / A x ) A • B = AB cos θ A•(B+C) = A•B + A•C A (B • C) = AB • C if A • B = 0, A┴B A X B = AB sin θ right thumb to first vector, fingers to second, palm=direction if A X B = 0, θ=0,π A•A= A x ² + A y ² + A z ² =A² îî = 1 ĵk = 0 EX. θ = ? A=3î+4ĵ-5k B=2î-3ĵ+3k A • B = AB cos θ cos θ = (A • B) / AB A•B=(3î 2î)-(4ĵ 3ĵ)-(5k 3k) = -21 A= √(3²+4²+5²) = √(50) B= √(2²+3²+3²) = √(22) cosθ = -21/(√(50) √(22)) θ = 129 COLLISIONS Ballistic pendulum: vb=(mb+mw)mb•2gh 1-D head on elastic collision therefore Ek'=Ek: va'=ma-mbma+mbva vb'=(2mama+mb)va Elastic: KE and P conserved Inelastic: only P conserved PIe:m1v1+m2v2=(m1+m2)vf PROJECTILE a x = 0 v x = v ox x = v ox t v ox = v o cos θ o t=xvicosθ a y = -g v y = v oy - gt y = v oy t - ½gt ² v oy = v o sin θ o y = (tanθ o )x – (____g_____ )x² (2v o ²cos ² θ o ) y max = v o 2 sin 2 θ/2g
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Formula Sheet - VECTORS COLLISIONS Ballistic pendulum:...

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