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# t1_2007_spring_retest_answers - MIME 2300 Test 1 Retest...

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MIME 2300 Test 1 Retest Name _______________________ Section ______ February 26, 2007 In all the problems show all equations used with variables and then with values substituted so partial credit can be given wherever possible. Give units on all answer. On problems where appropriate, draw coordinate systems, datums, FBDs, K.Ds or velocity diagrams. 1. A projectile is launched at 10 m/s from a sloping surface. The equation of the surface is 3 L L x y - = as shown. Determine the coordinates of the point of impact, x L and y L . ( 29 ( 29 t x t v x x 45 cos 10 0 45 cos 0 0 + = + = (1) ( 29 ( 29 2 2 0 0 2 81 . 9 45 sin 10 0 2 1 45 sin t t y gt t v y y - + = - + = (2) At impact ( 29 t x L 45 cos 10 = (3) ( 29 2 2 81 . 9 45 sin 10 t t y L - = (4) From equation for the landing surface 3 L L x y - = (5) Substitute (3) and (4) in (5) ( 29 ( 29 ( 29 3 45 cos 10 905 . 4 45 sin 10 2 t t t - = - ( 29 0 274 . 2 0 274 . 2 0 153 . 11 905 . 4 082 . 4 905 . 4 071 . 7 2 2 2 = - = - = - - = - t t t t t t t t t Solving for t, t=0s and t=2.274s. Therefore particle lands on surface at t=2.274s ( 29 ( 29 m x L 08 . 16 274 . 2 45 cos 10 = = m x y L L 284 . 9 3 08 . 16 3 - - = = - = Page 1 of 4 1 __________/32 2 __________/37 3 __________/31 Total ______/100 4 4 2(correct substitution of y 0 , and v 0 ) 2(correct substitution g) 4

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