问题 计算题

如图,滑板运动员在平台上从A位置水平滑出,在落到C位置时,运动员通过调整姿势进行缓冲使自己只保留沿圆轨道切向速度而不弹起。圆轨道光滑,O点为圆轨道圆心,C、E为等高点,OD为竖直线。已知:运动员与滑板的总质量M=90kg,AB=20m,BC=30m,

∠COE=600,g=10m/s,cos27o=0.9996求:

(1)滑板运动员从A位置滑出时的速度大小。

(2)滑板运动员从E位置滑出时的速度大小(结果保留两位小数)。

答案

(1)设滑板运动员从A位置滑出时的速度大小为Vo,从A位置滑至C位置的时间为t

BC=Vot        ①

AB=gt2            

V0="15m/s     "    ③

(2)设滑板运动员滑至C位置时速度大小为V1,运动员调整姿势后的速度为V2

mgAB=mV12-mV02     

V1="25m/s          " ⑤

设∠COD为α,V1与水平方向夹角为β,由几何关系得:

α=60o                           

β=53o                           

V2=V1cosβcosα+V1sinβsinα   ⑧

V2=m/s      ⑨

设滑板运动员从E位置滑出时的速度大小为V2,根据机械能守恒定律,得:

V3=V2="24.82m/s         " ⑩

阅读理解

根据短文内容,从短文后的选项中选出能填入空白处的最佳选项。选项中有两项为多余选项。

                                                                  1._____ 

     Most of us have one or a few bad habits that we'd like to get out of. But how do you do it? I have a few

suggestions that have helped me and people around me. Here are some tips that can help you to finally get out

of that bad habit. 

     2._____ If you tell people around you that you will stop smoking or start to exercise three times a week,

then they will check up on you. And you will feel you have to keep your promise because it is let out into the

world.

     Avoid temptations (诱惑). 3._____ Places where you are likely to spend too much money. Things in your

cupboard that will not help you to get healthier and you should not have at home at all. And people that drag

(拉) you down and back into your old ways. 

     4._____ It may seem like a good idea to change your life all at once. In our daily life, stress and lack (缺

乏) of energy usually lead to failure. Don't try to be Superman or Wonder Woman. Take it easy and break

one habit at a time. 

     5._____ You will probably not succeed the first time you do it. You fail and you make mistakes when you

make changes and try new things. That's just life and nothing to feel bad about. What you should do next is

try again.

A. Know what usually gets you into bad habits.

B. Simple tips for getting out of bad habits.

C. See your future in your mind.

D. If at first you don't succeed, please try again.

E. Tell your friends and family.

F. The reason why we need to make good habits.

G. Don't break more than one habit at a time.

单项选择题