sol ass4

# sol ass4 - PROBLEM 13.83 hA = 4300 km A R = 6370 km vA...

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PROBLEM 13.83 Knowing that the velocity of an experimental space probe fired from the earth has a magnitude 32.5 A v = Mm/h at point A , determine the velocity of the probe as it passes through point B . SOLUTION - At A , 32.5 M /h 9028 m/s A v m = = ( ) 2 6 1 9028 m/s 40.752 10 m 2 A T m = = × 2 A A A GMm gR m V r r = − = 6 10.67 M 10.67 10 m A r m = = × 6 6370 km 6.37 10 m R = = × ( )( ) ( ) 2 2 6 6 6 9.81m/s 6.37 10 m 37.306 10 10.67 10 m A V m m × = − = − × × At B 2 2 1 ; 2 B B B B B GMm gR m T mv V r r = = − = 6 19.07 M 19.07 10 m B r m = = × ( )( ) ( ) 2 2 6 6 6 9.81m/s 6.37 10 m 20.874 10 19.07 10 m B m V m × = − = − × × 6 6 2 6 1 ; 40.752 10 37.306 10 20.874 10 2 A A B B B T V T V m m mv m + = + × × = × 2 6 6 6 2 40.752 10 37.306 10 20.874 10 B v = × × + × 2 6 2 2 48.64 10 m /s B v = × 3 6.9742 10 m/s 25.107 Mm/h B v = × = 25.1Mm/h B v = W 4.3 6.37 A A r h R Mm Mm = + = + 10.67 A r Mm = 72.7 6.37 B B r h R Mm Mm = + = + 19.07 B r Mm = h A = 4300 k A B R = 6370 km v A v B h B = 12700

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= SOLUTION 0 .5 v θ = m /s, and 0 r v = . Neglecting the mass of the rod and the effect of friction, determine the radial and transverse components of the velocity of the collar when 120 r = mm .
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