COSMOS Chapter 3 Solution 58 - Edubirdie

University:
Michigan State University
Course:
ERG 160 | Success in Science, Technology, Engineering, and Mathematics
Academic year:

2020
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296

Pages:

1
Author:

lankstoetp16

COSMOS: Complete Online Solutions Manual Organization System Chapter 3, Solution 58. (a) For edge OA to be perpendicular to edge BC, uuur uuur OA ⋅ BC = 0 where From triangle OBC a 2 ( OA) x = ( OA) z = ( OA ) x tan 30° = a 1  a = 2  3  2 3 uuur  a   a  ∴ OA =   i + ( OA)y j +  k 2 2 3 and Then or so that uuur BC = ( a sin 30° ) i − ( a cos 30° ) k = a a 3 i− k 2 2 = a i − 3k 2 ( ) a a  a   =0  i + ( OA) y j +   k  ⋅ i − 3k 2 2 2 3   ( ) a2 a2 + ( OA)y ( 0 ) − =0 4 4 uuur uuur ∴ OA ⋅ BC = 0 uuur uuur OA is perpendicular to BC. (b) Have M OA = Pd , with P acting along BC and d the uuur uuur perpendicular distance from OA to BC. From the results of Problem 3.57, M OA = ∴ or . Pa 2 Pa = Pd 2 d = a 2

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