题目

某人在静水中游泳，速度为4千米/时，他在水流速度为4千米/时的河中游泳.（1）若他垂直游向河对岸，则他实际沿什么方向前进？实际前进的速度为多少？（2）他必须朝哪个方向游，才能沿与水流垂直的方向前进？实际前进的速度为多少？ 答案：解:（1）如图（1），设人游泳的速度为，水流的速度为，以、为邻边作OACB，则此人的实际速度为.由勾股定理知||=8,且在Rt△ACO中，∠COA=60°,故此人沿与河岸成60°的夹角顺着水流的方向前进，速度大小为8千米/时.（2）如图（2）,设此人的实际速度为，水流速度为，则游速为.在Rt△AOD中，||=4，||=4，||=4，cos       In spite of the instructions he had been given, Tommy did not hurry straight round to Mrs. Blakey’s house with the note. Reading the toy-shop window with its decorated Christmas tree, he could not tear himself away from it until he had spent ten minutes staring at the gift he most wanted: a gun that fired corks. Where the road began to run downhill to Mrs. Blakey’s house he met some of his friends who were throwing snowballs. He joined in the fight, and by the time it finished, another twenty minutes had gone by. Ten more minutes were lost looking for the note for Mrs. Blakey, which had somehow dropped from his pocket during the fight, When, with the help of his friends, his finally found it, it was not only very wet, but, to his horror, he found that part of it was torn way and missing. That meant a further search, but in vain. So it happened that, now looking very untidy, Tommy reached Mrs. Blakey’s house nearly an hour late and carrying a dirty piece of paper that contained only the words:                               for tea this afternoon                          important to talk about                         u. If it is inconvenient, tell Tommy; otherwise, ur house at four o’clock.                              Yours sincerely,                               Alice Hendry        Mrs. Blakey was puzzled over the note for a while, then, imagining she knew what the missing words were, told Tommy to tell his mother it would be all right.        Tommy returning home in much the same way as he had made the outward journey to Mrs. Blakey’s, arrived not long before four o’clock to find his mother very angry and already putting her hat on.        “You naughty boy, where have you been?” she cried, and without waiting for an answer, “What did Mrs. Blakey say?”        Tommy told her.        “All right, you’d better come with me,” Mrs. Hendry said．And so once again Tommy found himself on the downhill road to Mrs. Blakey’s.        At about the same moment that Mrs. Hendry and her son Tommy reached Mrs. Blakey’s door, Mrs. Blakey herself, having taken a different road, was waiting outside the Hendry’s home, wondering why there was no answer to her knock. Who could blame her for thinking that the torn note was an invitation to tea at the Hendry’s, instead of which Mrs. Hendry had in fact been asking herself out to tea with Mrs. Blakey? 1．In “he could not tear himself away from it” ‘it’ refers to________. A．Mrs. Blakey’s house                              B．the message C．the toy-shop window                            D．the road 2．Tommy’s mother told him_________        A．to hurry straight round to Mrs. Blakey’s house with the note        B  to play snowfight with the other kids        C．to look at the toy-shop window        D．to look for the note 3. Mrs. Blakey “told Tommy to tell his mother it would be all right” means_______.        A．she didn’t mind the note being torn        B．Mrs. Hendry’s request was inconvenient        C．she thought she could accept Mrs. Hendry’s invitation        D．she would find the missing words 4．Which of the statements is true according to the story?        A．After taking the note to Mrs. Blakey, Tommy hurried straight home        B．Tommy looked for the missing part of the note but could not find it        C．Mrs. Blakey guessed correctly what the missing words were        D．Mrs. Blakey expected to find Mrs. Hendry when she was going to her home at four o’clock