Throwing Darts (1)
Today, I went to the darts contest. I missed the first four and the last one. The teacher shook his head in disappointment. When I returned to the classroom, what I heard seemed to be the laughter of my classmates, and my heart suddenly dropped from high to O degree. I have been surrounded by pain. I wish there was a hole for me to get into.
Walking on my way home, I wanted to cry at the thought of it. Once again, I thought of the teacher's expression and the laughter of my classmates... The more I thought about it, the more sad I became. As soon as I got home, I got into bed and cried loudly. It seemed that a fairy in white came to me and said, "Son, there was a famous person who said two words:" Failure is the mother of success ", and" There must be setbacks in life, and you need to face them bravely ". Child, I hope you can do everything better. The white fairy disappeared with a sound of "wow". And me? Go to stare at the door, and finally understand.
Throwing Darts (2)
My mother and I prepared a book to record the scores. At the beginning, I got a zero egg for the first time, seven for the second time, seven for the first time, and zero for the second time. It has been a while since we were both high and low. My mother and I hope to win each other. In the last set, I lost and my mother won. I sighed, and my mother said, "Don't lose heart, and work harder next time." I laughed happily after hearing this.
Throwing Darts (3)
I wanted to go to the yard with Liu Dou after school this afternoon, but my mother refused to let me write a circular diary today. I heard it and cried hurriedly. My mother and I promised, "Isn't it just a circular diary? Isn't it just this math homework? I will finish it soon." Then my mother agreed. I was overjoyed to hear that, and immediately asked Liu Dou to go to the yard together.
On our way to the yard, Liu Dou picked up a flower shaped plastic sheet, which he said was plastic, but we called it a "dart"
As soon as we arrived at the yard, we threw the takeoff darts for fun. Throwing about, the dart was thrown into the flowers accidentally. Liu Dou said, "Where did you drop it?" I said, "I can't see it." "Come and find it if you have the ability!" "Well, come with me!" I said. I took Liu Dou to the flowers and said, "Right there." Liu Dou said, "Where is it?" I picked up the dart. Liu Dou immediately said, "Great!" We threw it back and forth again. Tired of playing, we went home to do our homework.
Throwing darts is really interesting! My family has a Frisbee. Liu Dou and I have an appointment to throw it tomorrow.
Throwing Darts (4)
When night falls, our family becomes particularly lively, and the family darts PK game begins!
First, introduce the members of the darts PK contest, including my father, my mother and me. The rule of dart PK is that three people throw darts in turn. The points of the three rounds are superimposed. The winner is the one with the highest score.
The game started. Dad went first. He picked up a dart, took a slight aim, and with a bang, the dart flew out. Unfortunately, the dart did not obey the command. After hitting 50 points, it fell off the target and jumped off the cliff to commit suicide. The father of the first escort got zero points. He was very depressed. Then I came on the stage, "Whew!" My red dart hit the target steadily. "V ten! I was proud and cheered for myself secretly. Mom was the last one to come on the stage. She said that she would not be the last one to throw anyway, so she threw the dart out, 60 points! No, her dart dropped from the original score of 60 points and was firmly fixed in the center of the target. In other words, Mom scored 100 points in the first game.
The second inning begins. Dad comes first. This time, he didn't dare to be careless. He aimed and then threw the dart out! Ninety points, quite good results. Then I threw 40 points and my mother threw 30 points. The scores of the first two innings add up. Dad scored 90 points, I scored 120 points, and Mom scored 130 points. Mom still ranked first.
At the crucial third round final, Dad calmly stood outside the line. He leaned forward, narrowed his eyes slightly, aimed at Baxin, and gently threw, "Bang!" Dad's dart hit the bull's-eye. He jumped three feet high and cheered loudly! Mom saw this and said, "Don't be too happy too soon. I can only throw 60 points to make a tie with you. Xian, let Mom come first." The more careful Mom was, the more her darts were disobedient. As a result, she only threw 50 points, failing to surpass Dad.
I'm on the court. I'm so nervous! I picked up the red darts, secretly made a wish, and then aimed and fired like my father, 70 points. yeah! The sum of my three innings is 190 points, which is just a draw with my father. I declare that I will be the first in the darts contest with my father, and my mother will be the second.
Why does my darts PK match sometimes go wrong? Ha ha, because the darts my father bought me are safe flat headed magnet darts! Because they are not pointed, they are attracted by magnets, so they sometimes slip off the target. If you want to play darts, come to my house and enjoy yourself!
Throwing Darts (5)
Some people like to play with pockets, some people like to jump rope, some people like to play with checkers... My favorite game is playing with darts.
People may think it's boring to play darts, but I can play with it. For example, stick a few notes on the board of a dart: watch TV for an hour, finish all your homework, play with the computer, wash dishes, mop the floor
I remember once I played darts with my father and mother. Mother came first, and she was very nervous. When she threw it, it turned out to be a dish washing note. Mother blushed and said, "Hmm... Hmm, this... this time doesn't count, let's do it again." Mother threw it again, but it was still washing the dishes. My father and I laughed, and Mother had to accept her fate. Next came my father and me. The note in my father's paper was to turn 30 circles in place and then walk in a straight line. My father first turned 30 circles and then walked in a straight line. After turning, he stumbled around and fell asleep when he hit the bed. And me? Throw a note of watching TV for an hour, I watched TV all night, I am really lucky!
I like playing darts, because it brings me endless fun and makes my home full of joy!
Throwing Darts (6)
Today, I bought many darts at home. The process is as follows: First, fold the paper in half. Second, fold it up and down. The third step is to fold the corners into small triangles. Step 4: Fold in half along the central line. Step 5: combine the two folded large Zs together. The beautiful darts are folded.
Throwing Darts (7)
Today is the last day of 2016, my mother took me to my cousin's house to play darts.
At the beginning, we tried to fly a few, and I found that I flew well, and two out of three, so I started the real race.
The elder sister was the first to shoot. She shot a two ring shot, which made a good start. I shot the second time. I shot a three ring shot, which was also good. I thought to myself: my sister and I both shot a good number of rings, and the younger brother should be at the 4th ring. My cousin started. His right foot was in front, his left foot was behind, and his front body was like a big shrimp. His left hand stretched forward in parallel, and his right hand grabbed the dart. When his hand was loosened, the dart flew out with a whoosh. I was watching intently and just heard "Ouch". I looked for my reputation and saw an "egg" growing on my mother's head. Ha ha, my mother happened to pass by when my cousin was sending darts, so this tragedy happened. Not this time, but again. This time, my sister threw it casually. Sadly, my sister won the ring 0, and it's a bad start. Will I also win the ring 0 next? I thought nervously. Because I am not the zero ring, I am serious. The left foot is in front, the right foot is behind, and the body is in front. When the right foot kicks, the hand is loosened, the dart flies out. Great, Ten Rings! Wait a minute, why is the dart not fixed? It slides down like a dance. Zero ring. Not to mention cousin, it is also zero ring. I found that whether we can get a good ring count depends on my sister. Sister is good, and we are all good; Sister got zero ring, and we all got almost zero ring.
Through this game, I learned that everything should be careful, as long as careful, you can succeed.
Throwing Darts (8)
I played darts with my father again this evening. Having learned the lesson of last failure, Dad became cautious. He picked up a dart, first aimed at the bull's eye, then tried again several times, and then shot it decisively. I saw that the dart flew to the target like an arrow and unexpectedly hit 9 rings. At this time, I was very worried and thought: Dad is going to win this game. But Dad didn't shoot well after two times and only hit 5 rings.
It's my turn. I'm nervous. I took the takeoff dart and shot it with force, but my three times' results added up to exceed my father's, and I won again. I'm so happy!
Throwing Darts (9)
This afternoon, my mother and I played the game of throwing darts on the balcony at home. My mother and I prepared a book to record the score and began to throw darts. I got zero eggs for the first time, seven points for the second time, zero eggs for the first time, and zero eggs for the second time. It has been a while since we were both high and low. My mother and I hope to win each other in the last set, but we may not win, In the end, I lost and my mother won. I sighed, and my mother said, "Don't lose heart, and work harder next time." I laughed happily after hearing this.
Throwing Darts (10)
Today, when I came home from school, I went to the supermarket to buy something. I saw many small plastic darts of different colors hanging on the wall. I thought it was very funny, so I asked how much it was. The old lady said 50 cents, and I bought one to take home.
I quickly returned home and opened the bag. The darts were blue. The appearance of the darts is the same as that in the cartoon Naruto. The front of the darts is sharp, and there is an iron circle behind. I took a piece of foam as the target.
I took the takeoff dart with my right hand. My middle finger was put on the circle of the dart. I threw it forward with all my strength. When I threw it, my middle finger loosened the circle of the dart. The dart flew out like a bow and arrow. Instead of flying into the foam, the dart flew to the iron thing and made a thump sound. I found a new way to play darts when I picked them up.
When I picked it up, I found that a dart can be turned into a dart with two corners and a dart with three corners. A dart with three corners should be called a boomerang instead of a dart. I changed the dart into a boomerang, which is more like a cartoon weapon. I grabbed a corner of the boomerang and threw it forward. The boomerang hit the foam, but it didn't break through. I think the plastic is too soft.
I had a good time today.
Throwing Darts (11)
Playing darts is a fierce game. Please come and see us playing darts!
Today, I played darts with several classmates. We were divided into two teams. I saw a classmate of the other side threw a dart. The dart was like a naughty child, flying right and left to our goal. The students who watched mentioned the noise in their hearts, and their mouths seemed to be sealed by tape, unable to speak. As a goalkeeper, I was so nervous that my heart jumped up and down like a rabbit, and my hands were sweaty. Because once the enemy breaks the door, their morale will be greatly boosted, which is unfavorable to our situation. So I decided to catch the dart. I am ready to fight. When the dart flew in, I kicked my feet and loosened my body like a spring. A "hungry tiger pounced on food" came. Unexpectedly, the dart suddenly turned and flew upwards. Seeing that the dart was about to enter the door, I was in a hurry and stretched my arm upward. Ah, it was blocked, and I danced happily. For our serve, a classmate served a "super high ball", and the other goalkeeper could not touch it by jumping hard, so he had to watch the ball enter the net. After that, the game entered a white hot stage, and the scores of the two teams rose alternately. The score was very tight, and no one could pull anyone more than 2 points. There is only one goal left. Now the score is 15:15. The students who watched held their breath. I saw the other team threw the dart over. I caught the dart easily, and then threw the dart to the other team's goal as quickly as I could. The other team was unprepared, so the dart entered the net. We won! Our team members sang and danced happily.
Today, I am so happy!
Throwing Darts (12)
Four days ago, Huayi Man was bullied by his neighbor and his enemy, Muscle Man.
In order to avenge him, he came up with a series of clever plans, but each of them had a common shortcoming, that is, each of them used force, and he could not defeat the muscular man. What shall I do? He originally bought a "darts game suit". He suddenly had a whim and marked all corners of the darts board with the words "muscular man". He thought about it, but he was too happy. He threw the dart and came back with a sad face. What happened again? The darts all pierced the gaps between the names. He doesn't believe in this evil. He threw it hard again. Unexpectedly, the door opened and the muscular man came in. The man who lost his muscle quickly responded. In a flash, the man who lost his muscle dodged. He was angry and shouted to the man in colored clothes: "Boy, if you dare to kill me, I will let the red pigment sprinkle all over your body." He squeezed the red pigment he carried with him, and the man in colored clothes was full of paint in his eyes and mouth. A muscular man will be beaten up.
Alas, the unlucky man in Huayi.
Throwing Darts (13)
Last year, my father came back from a business trip in Qingdao and gave my brother Mingming a pair of darts and a tennis racket. My favorite toy was darts. My father seems to have seen through my mind for a long time. This time, he went to Qingdao on business again and gave me a pair of darts. Looking at the long-awaited toy, I clapped my hands and jumped up happily.
Darts are composed of darts and targets. The dart consists of a dart tip, a dart pole and a dart wing. The dart tip is very sharp, which can firmly fix the dart on the dart target; The dart pole is used to connect the dart tip and the dart wing; The dart wing is used to balance the direction of the dart. The dart target is composed of nine black and white circles and a red bull's eye in the middle. They represent one to ten rings respectively.
When playing darts, you should first stand away from the bull's eye, then aim at the bull's eye with the dart and throw it with force, and finally calculate the score according to the circle hit by the dart. Since the dart flies in an arc, the dart should be slightly aimed at the top of the dart target when aiming, so that it can hit the bull's eye. When I first started playing darts, I often missed the target because I didn't master the skills. After repeated training, my performance was better and better each time. The process of playing darts made me understand the truth that practice makes perfect.
Playing darts can improve the coordination between hands and eyes, and cultivate our flexibility and accuracy in the game, so my favorite toy is darts.
Throwing Darts (14)
I like playing darts, because it brings me endless fun! The following is my composition about playing darts, which is carefully organized by this editor. I hope it can help you!
I like playing darts Composition 1:
Today, my father bought me a dart to play in my spare time.
My mother told me that the darts movement originated in the early 20th century. At first, it was just an entertainment activity in the bar. After the end of the First World War, with the emergence of the first brewery association, darts movement quickly became popular in the British Isles. In 1924, the British Throwing Darts Association took shape. Three years later, the first "News Cup" World Championship was officially held in London. Now? The professional darts association holds many wonderful competitions every year, such as the world competition, the world championship and so on, with many competitors.
After listening to my mother's words, I became more and more interested in darts. I quickly took a dart and shot it. I only shot six. My grandpa told me that throwing darts requires standing upright, lifting flat, aiming accurately, and requires full attention. At the moment of darting, the hand shakes slightly, or the mind has distractions, it is easy to miss. Then Grandpa gave me a demonstration.
Grandpa aimed at the bull's-eye, slightly adjusted the dart with his hand, then shook his right hand back and forth, and finally fired at the bull's-eye with his wrist. When I saw it, Grandpa threw 10 rings.
Then, I began to practice and learned the basic method of playing darts. Then, my family thought it was necessary to compete. Let me first say the rules of the game: ten rounds in a round, each player starts with 301 points, and the player's points decrease with the throw score. The player who first reduces the points to 0 wins. If no player reduces the points to 0 after ten rounds of throwing, the player with the lowest points wins. If the player who hits a dart reduces the points to the points that cannot end the game (points in the normal exit<0; points in the double area ≤ 1; points in the triple area ≤ 2 or points in the non double area/triple area reduced to 0 when hitting the double area/triple area under the condition of double area/triple area exit), it is "burst dart". After the burst dart occurs, cancel the round of points, and end the current round of throwing. It is the next player's turn to throw darts.
A fierce game has begun! I followed the original practice method and hit the bull's-eye. Later, they all went on stage once, and they were 9, 8 and 9 rings respectively. In the end, I won.
I like playing darts Composition 2:
Today, I went to my brother's house to throw darts.
Once I got to my brother's house, I went straight to the back room where I shot the darts.
There was a sound of "pa pa pa" in the distance. I went to see my brother playing with darts. He was holding the darts in his right hand, his left hand in his pocket, his body slightly tilted back, his right hand raised, slowly moved back, and then threw forward with force. The darts flew out. Only a sound of "pa" was heard, and the darts were firmly stuck in the third circle.
I was eager to try. When my brother saw me coming, he pulled me over and handed me the darts in his hand. The two darts were green and the two were red. My brother said to me, "Lin Yuqing, let's try it too." I leaned back slightly like my brother, raised my right hand and pulled it back, threw it forward forcefully, and the darts shot out. Because I was too impatient, He accidentally missed the target and inserted it into the wood. My brother looked at it and encouraged me. He said, "It doesn't matter if I missed the first shot. There are three darts behind me, and I hope you can shoot a satisfactory result." After listening to his encouragement, I got full breath, leaned back more, and pulled my hand more backward. I stared at the plate with my eyes fixed. I threw forward hard, and I hit the first circle! My brother looked at me and gave me a thumbs up sign. He said, "Look, this is not a shot. Your progress is really great!" After listening to my brother's praise, I became more confident. I once shot a dart, and this dart achieved a higher level than the previous one. I kept shooting and finally hit the bull's eye.
The circles one by one are like steps and darts one by one, just like our steps. Each shot is like our steps slowly moving towards the target of success.
Throwing darts is fun.
I like playing darts Composition 3:
On my decorative shelf, there is a little monk. My father bought them for me from Sichuan, and I like them very much.
The little monk is holding a meteor dart, which is only the size of his fist. He is practising martial arts! It's so lifelike. The little monk's head was shaved smooth and smooth to the touch. The cassock on his upper body is orange, and his lower body is wearing red training pants. His left leg is still up from the back, and his glasses are about to fall off. His mouth opened wide as if he was drooling. The only three hairs on his head are still dancing happily in the air. There are wrinkles on his forehead, which is because of the big eyes! I thought: Who makes him so fascinated? Following his eyes, oh, it was a graceful girl. Ha, what a naughty little arhat! He must be showing off his Kung Fu to the girl!
The little monk was standing on a green lawn. There was a tablet at the bottom left with three brown words "Meteor Dart" written on it. There was a very small pavilion on the right. The little monk had enough for twelve such pavilions. If you look at it carelessly, you will burst into laughter. Looking at the funny little monk, I can't help admiring the ingenuity of the master who designed the little monk.
I clean it with a rag every day, and then scrub it clean, and then put it away. Whenever I scrub it clean, it always smiles, as if thanking me for taking a bath for it, so as to win the girl's confidence. Guests who come to my house will be attracted by the small and exquisite monk and will give a "tuttut" of praise. And I always introduce it to the guests in detail.
This naughty little monk can eliminate the fatigue of a day's study and make the family full of laughter. I often think: Who designed this little monk? Later, I finally understood that it was designed by more than one person, but the common work of the people of the country! Knowing this, I like it even more!
Move: Meteor Throwing Dart - Whew
Throwing Darts (15)
Dart Shooting School Competition 200 (1)
Dart Shooting School Competition 200 (II)
Dart Shooting School Competition 200 (3)
Dart projection problem
1 Problem posing
In real life, people constantly pursue the accuracy of projection, and there are many similar problems in real life. However, due to the existence of air resistance in real life, there is no real oblique upward projection movement in reality, which is not as simple as the calculation of horizontal projection movement in middle school. It is very important for the dart shooter to find the appropriate angle and strength of projection.
2 Summary of model
The angle of dart projection, the initial speed of dart and the air resistance will affect the accuracy of dart projection and the number of hit rings. This paper first analyzes the trajectory of the dart's oblique upward throwing motion without considering the air resistance, so as to get the relationship between the initial speed and the angle of flight. Then, under the condition of considering the air resistance, it divides the horizontal and vertical directions, and uses the variable separation method of the first order differential equation to find the relationship between the speed and time, so as to get the relationship between displacement and time, Finally, the Newton tangent method is used to give the approximate solution, and the approximate solution is given. Finally, the relationship between the projection angle and the speed is obtained, and the method for estimating the error of the approximate solution is given, but the approximate solution is not estimated.
Keywords: air drag, oblique upcast motion, variable separation method, Newton tangent method, approximate solution error estimation.
3 Model Assumptions
(1) The dart is abstracted as a particle.
(2) The height of target release from the ground is h 1, and the height of dart target from the ground is h 2.
(3) The dart flies in a plane perpendicular to the ground, and the bull's-eye is also in that plane. (4) The time starts when the dart is released.
(5) For the convenience of calculation, it is assumed that the symbols in this paper do not have units and only represent simple quantities. (6) Darts rise first and then fall during flight, and the time of falling is very short.
4 Model establishment
(1) Without air resistance
Analysis: under the condition of no air resistance, the target is only subjected to gravity after release, and has an initial velocity of oblique upward, so the object is inclined upward. In the horizontal direction, make a uniform linear motion, and in the vertical direction, make a uniform deceleration linear motion with an acceleration of g.
Let the distance from the target when the dart leaves the projector be d, and the projection angle of the dart be
2 The speed is v0, and the flight time is t.
Horizontal direction: d ∨ v0cos t (4-1)
0 v0sin gt1 (4-2) Vertical direction:
Where, t1 is the time when the dart reaches the highest point from releasing to decelerating to zero, and g is the acceleration of gravity, which is a known constant.
If the flight altitude from releasing to flying to the highest point is h, then
one
hgt12 （4-3）
two
The flight altitude from high point to flight stop is
twelve
（4-4） hh1h2gt2
two
Where t2 is the time from the highest point of the dart to the target surface.
While d, h1 and h2 are measurable and can be regarded as known quantities, so the relationship between v0 and can be obtained from equations (4-1), (4-2), (4-3) and (4-4) as follows:
two
v0sin2vsin21d h1h2g(0)
2g2v0cosg
(2) Under the condition of air resistance
Analysis: the horizontal direction decelerates due to the existence of air resistance, and since the air resistance is proportional to the speed, the air resistance is variable. From the calculation formula of air resistance, f ∨ kv (k is the air friction coefficient, which is related to the air density), it can be seen that the deceleration movement in this direction is gradually reduced in acceleration; In the vertical direction, the acceleration in the vertical direction will gradually decrease, and when it reaches the highest point, it will move downward. Since the initial speed is zero, the formula f ∨ kv shows that the air resistance will be less than the gravity of the object for a period of time, until the air resistance and gravity are equal, the balance of forces in the vertical direction will continue to move vertically downward at a uniform speed in a straight line. But we assume that the falling time is very short, so when the dart falls on the target surface, it has not reached the moment of f ∨ mg. In the horizontal direction, we have:
dv1kv
1 dtm
Where, v1 is the velocity in the horizontal direction. Using the variable separation method of the first order differential equation, we can get:
kt
∨ c1 (c1 is a fixed constant) m
In particular, when t ∨ 0.
lnv1
(0cos) c1lnv
Further, by introducing c1 into the above equation, we can get: v1 ≮ v0cos e
kt
m
By integrating t with the above equation, we can get:
ktm
sv0cose
t
dt
Let the right end of the above equation equal to d, and we get the total flight time of the dart, t ∨
mkdln1() kmv0cos
In the vertical direction, it is assumed that the dart first makes a vertical upward deceleration motion with gradually decreasing acceleration, and finally
Decelerate to zero. Therefore:
dv2mgkv2
dt1m
Where v2 is the speed of the dart when it rises. Using the variable separation method of the first order differential equation, we can get: lnkv (2 ∨ mg) ∨ -
kt1
∨ c2 (c2 is a fixed constant) m
In particular, when t1 ∨ 0, c2 ∨ ln (kv0sin ∨ mg) further, bring c2 into the above equation to get:
11
v2[(kv0sinmg)emmg]
k
kt
Let v2 ∨ 0 to get the total time t of darts rising, total 1 ∨ - integrate t1 on both sides of the above equation to get: h h1 ∨
t1
mmg
ln
kkv0sinmg
11
kv0sinmg)emmg]dt1 k
kt
mv0sinm2gmg
∨ 2ln ∨ h1 Take the value of t total 1 into the above equation, and then we can get h ∨
Kkv0sin ∨ mgk From the analysis, it is known that after passing the highest point, gravity and air resistance are reversed, and gravity is greater than
Air resistance, so the dart starts to accelerate with decreasing acceleration. Therefore:
dv3mgkv3
dt2m
Where, v3 is the speed of the dart when it descends. Using the variable separation method of the first order differential equation, we can get:
(kv3) lnmg
kt2
∨ c3 (c3 is a fixed constant) m
T2 starts timing after passing the highest point. In particular, when t2 ∨ 0, v3 ∨ 0, c3 ∨ lnmg()
Further, by introducing c3 into the above equation, we can get:
2mg v3(1em)
k
kt
By integrating t2 on both sides of the above equation, we can get: h h2 ∨ and x ∨
kt2
m
t2
2mg
(1em)dt2 k
kt
mv0sink2m2gemg
hhln c2212 kvsinmgkmgk0
Then the following equation can be obtained:
x ∨ ex ∨ c ∨ 0 (4-5) For the solution of this equation, the Newton tangent method is used to give an approximate solution. If f ∨ x ∨ ∨ x ∨ ex ∨ c, there will be f '∨ x ∨ ∨ 1 ∨ ex, f "∨ x ∨ ex
First, make a qualitative estimation of t2. From the question, the falling time t2 with air resistance should be less than the total flight time, that is:
mkd
() t2ln1kmv0cos
According to the analysis of II, during the falling process, kv3 is mg, so the acceleration during the falling process is always less than 2g
twelve
At and falling height h h2 Given, total falling time t2 ＞ 2
hh2
Then respectively set g
aln1(
kdkhh2
)，b。
Throwing Darts (16)
This afternoon, my mother and I played the game of throwing darts on the balcony at home.
My mother and I prepared a book to record the scores and began to throw darts. I got zero eggs for the first time, seven points for the second time, five points for the first time, and zero eggs for the second time. It has been a while since we were both high and low. My mother and I hoped to win each other in the last set, but we may not win. Finally, I lost, Mom won. I sighed, and my mother said, "Don't lose heart, and try again next time."
After hearing this, I smiled happily.
