问题 选择题

如图1所示,质量为的小车在光滑的水平面上以速度向右做匀速直线运动,一个质量为的小球从高处自由下落,与小车碰撞后反弹上升的高度为仍为。设,发生碰撞时弹力,小球与车之间的动摩擦因数为,则小球弹起时的水平速度可能是

.                  .

.            .

答案

AC

:小球的水平速度是由于小车对它的摩擦力作用引起的,若小球在离开小车之前水平方向上就已经达到了,则摩擦力消失,小球在水平方向上的速度不再加速;反之,小球在离开小车之前在水平方向上就是一直被加速的。故分以下两种情况进行分析:

小球离开小车之前已经与小车达到共同速度,则水平方向上动量守恒,有

由于

所以   

若小球离开小车之前始终未与小车达到共同速度,则对小球应用动量定理得

水平方向上有

竖直方向上有

解以上三式,得

故,正确的选项为AC。

阅读理解

阅读理解。

     Inside the pleasingly fragrant cafe, So All May Eat(SAME) in downtown Denver ,the spirit of

generosity(慷慨)is instantly noticeable :A donation box stands in place of a cash register. Customers

here pay only what they can afford, no questions asked. A risky business plan, perhaps, but SAME Caf?

has done one unchangeable thing in the Mile High City for six years: Open only at midday, the restaurant

provides poor local can instead volunteer as waiters and waitresses, and dishwashers, or took after the

buildings and equipment for the cafe.

    "It's based on trust, and it's working all right" , says co-owner Brad Birky , who started the cafe in

2006. With his wife Libby. Previously volunteering at soup kitchens, the Birkys were dissatisfied with the

often unhealthy meals they served there. "We wanted to offer quality food in a restaurant where everyone

felt comfortable ,regardless of their circumstances," Birky says. SAME's special lunch menu changes daily and most food materials are natural and grown by local farmers. The cafe now averages 65 to 70

customers (and eight volunteers) a day. And the spirit of generosity behind the project appears to be

spreading. In early 2007,one volunteer who had cleared snow for his meals during the long winter said

goodbye to the Birkys," He said he was going to New Orleans to help with the hurricane clear up," says

Birky. 68.What can we learn about the soup kitchens the Birkys previously worked for?

1. What can we learn about the soup kitchens the Birkys prcviously worked for?

A. hey refused to have volunteers.

B.  They offered low quality food.

C. They provided customers with a good environment.

D. They closed down because of poor management.

2.  According to the passage, which of the following is TRUE?

A. The customers who cannot pay can word as volunteers in stead.

B. More volunteers will go to new Orleans for the hurricane cleanup.

C. Many new cafes will be opened to offer free lunches in the town.

D. The lunch menu has remained the same since the cafe was started.

3.  The author's attitude towards running such a caf? is_______

A. unfavorable   

B. approving

C. doubtful

D. cautious

填空题

阅读以下说明和C代码,将应填入 (n) 处的字句写在对应栏内。

[说明]

函数combine(a,b,c)是计算两个整数的组合数。由于计算结果可能超出10ng整型的可表示范围,故采用数组方式存储,例如:k位长整数m用数组c[]存储结构如下:m=c[k]×10k-1+c[k-1]×10k-2+…+c[2]×10+c[1],利用c[0]存储长整数m的位数,即c[0]=k。数组的每个元素只存储长整数m的一位数字,长整数运算时,产生的中间结果的某位数字可能会大于9,这是就应该调用format将其归整,使数组中的每个元素始终只存储长整数的一位数字。

整数a和b(a>b)的组合数为:,其中u1=a,u2]=a-1,…,ub=a-b+1,d1=1,d2=2,…,db=b。为了计算上述分式,先从u1,u2,…,ub中去掉d1×d2×…×db的因子,得到新的u1,u2,…,ub,然后再将它们相乘。

[函数]

#define NAXN 100

int gcd(int a,int b)//求两个整数a和b的最大公因子

{

if(a<b){

intC=a;a=b;b=c;

}

for(inti=b;i>=2;i--){

if( (1) )return i;

}

return 1;

void format(int *a)//将长整数数组归整

{

int i;

for(i=1;i<a[0]||a[i]>=10;i++){

if(i>=a[0]) (2)

a[i+1]+=a[i]/10;

a[i]=a[i]%10;

}

if(i>a[0]) (3)

}

void combine(int a,int b,int *C)

{

int i,J,k,x;

int d[MAXN],u[MAXN];

k=0;

for(i=a;i>=a-b+1;i--)u[++k]=i;

u[0]=b;

for(i=1;i<=b;i++)d[i]=i;

for(i=1;i<=u[0];i++){//从u中各元素去掉d中整数的因子

for(j=1;j<=b;j++){

x=gcd(u[i],d[j]);//计算最大公约数

u[i]/=X;

d[j]/=x;

}

(4) ;C[1]=1;//长整数c初始化

for(i=1;i<=u[0];i++)(//将u中各整数相乘,存于长整数c中

if(u[i]!=1){

for(j=1;j<=c[0];j++){

C[j]= (5)

}

format(C);//将长整数c归整

}

}

}

(4)处填()。