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Analytical Mech Homework Solutions 57

Analytical Mech Homework Solutions 57 - v = zv yi zvx yvx k...

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ˆ ˆ ˆ z y z x y x v v i v j v ω ω ω ω k × = − + G G G G v j ( ) ˆ ˆ z y z x horiz v v i ω ω ω ′ ′ × = − + ( ) ( ) ( ) 1 1 2 2 2 2 2 2 2 2 z y z x z x y z horiz v v v v v ω ω ω ω × = + = + = G G G G G v ω v 2 cor F m ω = − × G ( ) ( ) 2 cor z horiz horiz F m v m 2 v ω ω = × = G G , independent of the direction of v . G ′ ′ 5.13 From Example 5.4.1 … 1 3 2 1 8 cos 3 h h x g ω λ ′ = and 0 h y ′ = . ( ) 1 3 3 2 5 1 2 1 8 1250 7.27 10 cos41 3 32 h ft x s ft s × ′ = × D 0.404 h x ft ′ = to the east. 5.14 From Example 5.4.2: 2 sin H v ω λ ∆ ≈ D is the deflection of the baseball towards the south since it was struck due East at Yankee Stadium at latitude (problem 5.13). v 41 N λ = D 0 is the initial speed of the baseball whose range is H. From eqn 4.3.18b, without air resistance in an inertial reference frame, the horizontal range is … 2 sin 2 v H g α = D Solving for v 0 1 2 sin 2 gH v α
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