How long does a ball stay in the air when thrown 10m high?

The acceleration of a ball is constant; it is called gravity acceleration and is denoted as `g approx 10 m/s^2.` It is directed downwards.

The upward vertical speed of a ball uniformly decreases until it becomes zero, and a ball reaches its maximum height at that moment. Then the vertical speed becomes downward and increases uniformly. The general formula is `V(t) = V_0 - g t,` where `V_0` is the initial upward speed. So the time...

The acceleration of a ball is constant; it is called gravity acceleration and is denoted as `g approx 10 m/s^2.` It is directed downwards.

The upward vertical speed of a ball uniformly decreases until it becomes zero, and a ball reaches its maximum height at that moment. Then the vertical speed becomes downward and increases uniformly. The general formula is `V(t) = V_0 - g t,` where `V_0` is the initial upward speed. So the time needed to reach a maximum height is `t_1 = V_0/g.`

The formula for height is `H(t) = V_0 t - (g t^2)/2.`  Thus the maximum height is `H_(max) = H(t_1) = V_0^2/(2g).` It is given, so we can find `V_0 = sqrt(2gH_(max)).`

A ball falls at the moment `t_2gt0` at which `H(t_2) = 0,` so `t_2 = (2V_0)/g.` Substitute the formula for `V_0` and obtain `t_2 = 2sqrt((2H_(max))/g) approximately 2.8(s).` This is the answer.

What message did the traveler leave in the poem "The Listeners" by Walter de la Mare?

The message that the traveler leaves to "the listeners" of the house is that he came to the house exactly like he said he would.  

The answer to this question can be found within the final third of the poem.  The traveler has arrived at a lone house.  It is nighttime, and the moon bathes the house in light.  It's definitely an eerie setting and circumstance.  It is made even more eerie by the...

The message that the traveler leaves to "the listeners" of the house is that he came to the house exactly like he said he would.  

The answer to this question can be found within the final third of the poem.  The traveler has arrived at a lone house.  It is nighttime, and the moon bathes the house in light.  It's definitely an eerie setting and circumstance.  It is made even more eerie by the fact that nobody seems to be in the house.  It is empty for some unknown reason.  If it isn't empty, then the occupants are intentionally staying completely silent while the traveler repeatedly knocks on the door.   Eventually, the traveler gives up on waiting for someone to answer the door.  Before he leaves though, he says to nobody in particular the following lines.  

‘Tell them I came, and no one answered,   

   That I kept my word,’ he said. 

What point of view is represented in Burr by Gore Vidal?

"Burr" is an iconic novel by author Gore Vidal that focuses on the true history of the Founding Fathers of the United States of America. The story is told from the point of view of a young Charles Schuyler, a twenty-five-year-old man who served as a law clerk in Aaron Burr's office. Burr was the third Vice President of the United States, serving alongside President Thomas Jefferson during his first term. The decision to tell the story of "Burr" from young Schuyler's point of view is an interesting one, as Vidal uses Schuyler's youthful naïveté and optimism to shine a light on the more scandalous aspects of Burr's service.

Through Schuyler's eyes, the reader is able to see Burr as he really was, a figure surrounded by more controversy and moral dilemmas than his relatively sanitized portrayal in the average history textbook would suggest. The story begins in 1833 and tells of Schuyler's exploits as Burr's clerk, and ends four years after the former Vice President's death. Burr's perspective is made all the more intriguing by the fact that he hopes to abandon his life of politics to become a professional writer.

Schuyler is at first enamored with the sophisticated politician and envies his worldly qualities. As "Burr" continues, his naïveté is shattered and be begins to realize that the man does not fully live up to his public reputation. Through a variety of political schemes and vices, Schuyler is indoctrinated into the world of political intrigue and the reader experiences it all through his first person perspective.

The use of first person point of view allows Vidal to inject a significant amount of humor and personality into the narration. Schuyler's voice is witty and full of enthusiasm, making "Burr" an engaging read from the first page. Observations about the other characters, such as "Shortly before midnight, July 1, 1883, Colonel Aaron Burr, aged seventy-seven, married Eliza Jumel, born Bowen fifty-eight years ago (more likely sixty-five, but remember: she is prone to litigation!)" offer humorous insights into the various ways in which their personal lives contradict the public images they project.

"Burr" is an excellent example of the use of first person point of view that lends personality to a narrative that might otherwise feel dry or forced if told from an impersonal third person point of view. Having Burr's story told from someone close to him also allows Vidal to delve into his exploits with greater honesty and sympathy than if he had written it from Burr's point of view or that of an omniscient narrator.

If the length of a wire of resistance `R` is uniformly stretched to `n` times its original value, what will be its new resistance?

I suppose that the cross sectional area `A` of the original wire is constant along its length, and the same for the stretched wire (although its cross sectional area `A'` is clearly different).

It is known and is not of big surprise that the resistance of a wire from the same material in the same conditions is directly proportional to its length `L` and is inversely proportional to its cross sectional area `A.`

It is...

I suppose that the cross sectional area `A` of the original wire is constant along its length, and the same for the stretched wire (although its cross sectional area `A'` is clearly different).

It is known and is not of big surprise that the resistance of a wire from the same material in the same conditions is directly proportional to its length `L` and is inversely proportional to its cross sectional area `A.`

It is given that the new length `L'` is `n` times greater than the original, `L'=n*L.` What about the new cross sectional area `A'?` The mass of the wire and therefore its volume must remain the same, and it is equal to `L*A = L'*A' = n*L*A'.` Hence the new area `A' = A/n,`  `n` times less, and

`(L')/(A') = (nL)/(A/n) = n^2 L/A.`

Therefore the new resistance will be `n^2` times greater than the original, `R' = n^2 R.`

Could the rats in The Problem of Cell Thirteen reasonably be called Van Dusen's helpers?

The rats could reasonably be called Van Dusen's helpers. Van Dusen bet Dr. Ransome and Mr. Fielding that he could escape from any prison. They arranged for Van Dusen to be held at Chisholm Prison. Van Dusen promised that he would escape from the prison in a week's time and that they would meet for dinner at his place after his escape.

Van Dusen was escorted to the prison by Dr. Ransome and Mr. Fielding....

The rats could reasonably be called Van Dusen's helpers. Van Dusen bet Dr. Ransome and Mr. Fielding that he could escape from any prison. They arranged for Van Dusen to be held at Chisholm Prison. Van Dusen promised that he would escape from the prison in a week's time and that they would meet for dinner at his place after his escape.

Van Dusen was escorted to the prison by Dr. Ransome and Mr. Fielding. They met the warden, who was earlier informed of the experiment. The terms of the experiment were explained and Van Dusen took the opportunity to request some items. He was then ushered into cell 13, which was considered very secure.

While in his cell, Van Dusen stumbled upon a hole in the wall that was connected to the prison’s old drainage system. His discovery was made possible by rats who visited his cell from outside the prison walls through the drainage system. He later used one of the rats to deliver a message to Mr. Hatch, who worked for a media company and also served as his accomplice in the elaborate escape.

There were at least half a dozen rats in the cell -- I could see their beady eyes. Yet I had noticed none come under the cell door. I frightened them purposely and watched the cell door to see if they went out that way. They did not, but they were gone. Obviously they went another way. Another way meant another opening.

How can you tell from the story that the policeman is Jimmy in "After Twenty Years"?

Jimmy's letter shows he was the policeman who conversed with Bob in the beginning of the story.

In the letter, Jimmy mentions he was on time to meet Bob. While speaking with him, however, he recognized Bob as a criminal wanted by Chicago cops. Jimmy asks a plainclothes officer to impersonate him because he can't bring himself to arrest a man he used to call a friend.

I didn’t want to arrest you myself. So...

Jimmy's letter shows he was the policeman who conversed with Bob in the beginning of the story.

In the letter, Jimmy mentions he was on time to meet Bob. While speaking with him, however, he recognized Bob as a criminal wanted by Chicago cops. Jimmy asks a plainclothes officer to impersonate him because he can't bring himself to arrest a man he used to call a friend.

I didn’t want to arrest you myself. So I went and got another cop and sent him to do the job.

The contents of the letter make it clear Jimmy was the police officer. As we look back at the story, the letter explains why Jimmy asked how long Bob was willing to wait:

“I’ll go on my way,” he said. “I hope your friend comes all right. If he isn’t here at ten, are you going to leave?” “I am not!” said the other. “I’ll wait half an hour, at least. If Jimmy is alive on earth, he’ll be here by that time. Good night, officer.”

Based on Bob's answer, Jimmy may have concluded half an hour was plenty of time for another officer to impersonate him and meet with Bob.

Bob's answer also shows he still has some affection for his old friend, Jimmy. The men may not be close now, but past memories and shared experiences are often difficult to forget. This is perhaps the reason Jimmy sends another officer to do his job.

What are two outside sources about how Huck Finn's views toward Jim, society, or his conscience change in The Adventures of Huckleberry Finn?

One source about the changes in the character of Huck Finn is the article "The Flawed Greatness of Huckleberry Finn," published in Mizzou Magazine on May 21, 2013 (see the link below). Written by Twain scholar Tom Quirk, an English professor at University of Missouri, the article discusses the flaws in Huckleberry Finn's characters. The author argues the flaws help Twain create real characters. As the author states,

Mark Twain often submerged himself in...

One source about the changes in the character of Huck Finn is the article "The Flawed Greatness of Huckleberry Finn," published in Mizzou Magazine on May 21, 2013 (see the link below). Written by Twain scholar Tom Quirk, an English professor at University of Missouri, the article discusses the flaws in Huckleberry Finn's characters. The author argues the flaws help Twain create real characters. As the author states,

Mark Twain often submerged himself in and submitted to the voices of his created characters, the lowliest of the low, a 'community of misfortune' as he later called the pair, and let them speak for themselves. In other words, Huckleberry Finn is the supremely democratic novel, at least it is when Twain stays out of the way.

In other words, while Huck Finn is far from perfect, he is real because Twain allows him to speak for himself. Quirk pays particular attention to Chapter 9 of Huckleberry Finn, in which Huck covers up his father's dead body so Jim doesn't see it. This is an example in which Huck's views of Jim and of slavery change. The scene is in part a reference to the story of Noah and Ham in the Bible. Ham, Noah's son, did not cover up his father's naked body, and Noah later cursed Ham, which was used as a Biblical justification for slavery because slaves were regarded as the descendants of Ham. Therefore, this passage is an example of Huck regarding Jim with care and deference. The scene also refutes the justification of slavery.

Another outside source is "Rethinking Huck" by Steven Mintz in "History Now," the Journal of the Gilder-Lehrman Institute (at the link below). The article examines the inconsistencies in the novel to discuss whether Huck is racist. Mintz writes,

Huck hates abolitionists, and yet in the book’s most poignant scene, the book’s moral center, he apologizes to Jim for the indignities he has inflicted. Admits Huck: "I done it and I warn’t ever sorry for it afterwards." Yet this is also a book without a clear, unambiguous hero.

Although Huck is at times a victim of his racist society, Mintz argues the reader has to appreciate how much entrenched racism Huck must overcome in his mind and world in order to regard Jim as an equal. Huck's apology to Jim is a significant act in Huck's racist world. Mintz says, "At the novel’s very heart lies the conflict between Huck Finn’s instincts and his conscience, which had been deformed by his upbringing." In other words, Huck's journey towards seeing Jim as a human being is greater and more significant because it is so hard for Huck, as he comes from a society that degrades black people.