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t1_2007_spring_answers

t1_2007_spring_answers - MIME 2300 Test 1 Name Section In...

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MIME 2300 Test 1 Name _______________________ Section ______ February 16, 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. In practice, the quarterback throws the football with velocity v 0 at 45° above the horizontal. At the same instant, the receiver standing 20 ft in front of him starts running straight downfield at 10 ft/s and catches the ball. Assume that the ball is thrown and caught at the same height above the ground. What is the velocity v 0 ? (28 points) Solution: Coordinate system at quarterback ( 29 t 45 cos v x x 0 ball _ 0 ball ° + = ( 29 t 45 cos v 0 x 0 ball ° + = (1) t v x x receiver _ 0 receiver _ 0 receiver + = t 10 20 x receiver + = (2) When ball is caught receiver ball x x = ( 29 t 45 cos v t 10 20 0 ° = + (3) One equation with 2 unknown so need an additional equation ( 29 2 0 ball _ 0 ball gt 2 1 t 45 sin v y y - ° + = ( 29 2 0 t 2 . 32 2 1 t 45 sin v 0 0 - ° + = (4) Solve equation (4) for v 0 ( 29 ( 29 ° = ° = 45 sin t 1 . 16 t 45 sin t 1 . 16 v 2 0 Substitute v 0 into equation (3) ( 29 ( 29 t 45 cos 45 sin t 1 . 16 t 10 20 ° ° = + ( 29 ( 29 0 20 t 10 t 45 sin 45 cos 1 . 16 2 = - - ° ° 0 20 t 10 t 1 . 16 2 = - - Use quadratic formula 846 . 0 , 468 . 1 t - = Negative has no physical significance 468 . 1 t = Substitute t into equation (4) s / ft 4 . 33 v 0 = Page 1 of 4 1 __________/28 2 __________/36 3 __________/8 4 __________/28 Total ______/100 Solve equation (4) for t ( 29 1 . 16 45 sin v t 0 ° = Substitute t into equation (3) ( 29 ( 29 ( 29 1 . 16 45 sin v 45 cos v 1 . 16 45 sin v 10 20 0 0 0 ° ° = ° + ( 29 ( 29 ( 29 0 20 v 1 . 16 45 sin 10 v
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