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PROPRIETARY MATERIAL. © 2013 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed, reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. If you are a student using this Manual, you are using it without permission. 171 PROBLEM 11.115 An oscillating garden sprinkler which discharges water with an initial velocity v0 of 8 m/s is used to water a vegetable garden. Determine the distance d to the farthest Point B that will be watered and the corresponding angle α when (a) the vegetables are just beginning to grow, (b) the height h of the corn is 1.8 m. SOLUTION First note 0 0 0 0 ( ) cos (8 m/s) cos ( ) sin (8 m/s) sin x y v v v v α α α α = = = = Horizontal motion. (Uniform) 00 ( ) (8 cos )xx v t tα= + = At Point B: : (8 cos )x d d tα= = or 8 cosB d t α = Vertical motion. (Uniformly accelerated motion) 2 0 2 2 1 0 ( ) 2 1 (8 sin ) ( 9.81 m/s ) 2 yy v t gt t gt gα = + − = − = At Point B: 21 0 (8 sin ) 2B Bt gtα= − Simplifying and substituting for Bt 1 0 8 sin 2 8 cos d gα α = − or 64 sin 2d g α= (1) (a) When 0,h = the water can follow any physically possible trajectory. It then follows from Eq. (1) that d is maximum when 2 90α = ° or 45α = ° Then 64 sin (2 45 ) 9.81 d = × ° or max 6.52 md =