PHYSICS: Free Fall

A free falling object is an object that is falling under the sole influence of gravity. Any object that is being acted upon only by the force of gravity is said to be in a state of free fall. There are two important motion characteristics that are true of free-falling objects:

• Free-falling objects do not encounter air resistance.
• It accelerates downwards at a rate of 9.8 m/s².

Because free-falling objects are accelerating downwards at a rate of 9.8 m/s², a dot diagram of its motion would depict acceleration. The dot diagram at the right depicts the acceleration of a free-falling object. The position of the object at regular time intervals – say, 0.1 second is shown. The fact that the distance that the object travels every interval of time is increasing is a sure sign that the ball is speeding up as it falls downward. An object travels downward and speeds up, and then its acceleration is downward.

Uniform Gravitational Field without Air Resistance

Where:
     v₀ – is the initial velocity (m/s)

     v(t) – vertical velocity with respect to time (m/s)

     y₀ – initial altitude (m)

     y(t) – altitude with respect to time (m)

     t – time elapsed

     g – acceleration due to gravity

Problem ~

An object in free fall is said to have reached terminal velocity. If the air resistance becomes strong enough to counter act all gravitational acceleration, causing the object to fall at a constant speed. The exact value of the terminal velocity varies according to the shape of the object, but can be estimated for many objects at 100m/s. When a 10kg object has reached terminal velocity, how much power does the air resistance exert on the object?

Solution:
To solve this problem, we will use the equation P = Fv cos θ instead of the usual power equation, as we are given the velocity of the object. We merely need to calculate the force exerted on the object by the air resistance, and the angle between the force and the velocity of the object. Since the object has reached a constant speed, the net force on it must be zero. Since there are only two forces acting on the object, gravity and air resistance, the air resistance must be equal in magnitude and opposite in direction as the force of gravity. Thus, F_a = - F₆ = mg 98N , pointing upwards. Thus, the force applied by air resistance is anti-parallel to the velocity of the object. Thus:

Sources: www.physicsclassroom.com/

www.sparknotes.com/physics/workenergypower/

PHYSICS: Projectile Motion

Projectile motion refers to the motion of an object projected into the air at an angle. A projectile is an object upon which the only force acting is gravity. Objects launched are called projectiles.

History:

Niccolo Tartaglia shows it was realized that projectiles actually follow curved path. Yet no one knew what that path was, until Galileo Galilee. First, he reasoned that a projectile is not only influenced by one motion, but two. The motion that acts vertically is the force of gravity that pulls an object towards the earth at 9.8 m/s². While having this motion, the projectile is also moving forward, horizontally at the same time. And this horizontal motion is uniform and constant according to Galileo’s principle of inertia. This two independent motions of him work together to create a precise mathematical curve – mathematical shape, a shape from Greeks called parabola.

Parabolic motion has the following properties.

1. They are under constant acceleration.
2. There, exists a non-zero component which is perpendicular to the acceleration so as to produce a parabolic path. If this condition is not satisfied, the motion is actually a linear motion. 

Basic Equations:

Horizontal velocity = u cos θ

Vertical velocity = u sin θ

The horizontal and vertical displacements of the objects are:

            (x) Horizontal displacement at time =  

            (y) Vertical displacement at time =

To find the maximum height:

So from dy/dx = 0, we get u sin θ – gt = 0

Sub (1) into the vertical displacement equation:

Equation of Trajectory:

From above, we know that:

            Horizontal motion (x) =

                                 

            Vertical motion (y) =  

                   

Eliminating t, we get

                          

This equation can be transformed to a quadratic equation in tan a

FORM OF EQUATIONS	USES
	1.        Find out the position of an object at a particular time. 2.      Find out the time taken for an object to travel to particular position.
	1.        Find out the y-position by given other condition. 2.      Find out the x-position by solving this quadratic equation.
	1.        Find out the angle of projection. 2.      Determine the minimum velocity of projection to clear an obstacle.

Source: www.library.thinkquest.org/

Pay It Forward.

Watching this film all over again, the more I understood the sense of the story. And there’s this story I remember that is more likely to this, the movie Milk in the year 2008. The difference was that the lead character is more mature at the age of 40, and is homosexual (it’s actually a true story about an American politician, Harvey Milk). But the exceptional thing to these movies, they have the same objective. They want to let us know that being a kid (or even fully grown) is not a thing about changing the world.

You don’t need to grow up first to change the world or trying to return your childhood. You don’t have to because it isn’t about being old or young. It’s always within oneself. By putting your perception into action, could make a big change. Change in you, your family, friends, relatives, until to the world.

I do really love the story, as well as the individuality of the lead character and its teacher. The story starts with a question, “What does the world mean to you?” and the class thinks. Then Mr. Simonet asked again, “What does the world expect of you?” Trevor answered, “Nothing.” That line really knocked me; because really, I don’t even know what does the world expect from me! I don’t even know how I can contribute a thing to this world.

The world for me is a family, my family, other’s family. Well, that’s the point, I mean, beginning of being you, yourself, or being/having [molding] one’s individuality. A loving parents, courteous relatives, adorable cousins… a much supported childhood. How lucky am I to have them? Always ready to help me in times of trouble.

Isn’t that great to visualize the world like my family? Though I know that it’s not always perfect, there’s at times (and won’t just disappear) that problems will get a way in. But there are a lot of reasons to hold on, a lot of reasons to stay, and reasons to change. Change not only inside of you, but inside of your family. We’re having problems to think of solutions, not of problems again. [From somebody]

And this one’s strange… Mr. Simonet asked for an assignment: “Think of an idea to change our world – and put it into ACTION!” Why? He knows that his class thinks of the world expects nothing from them as they were just seventh graders. Then why would he give an assignment about changing the world? Yes, and there goes, “Weird… crazy… hard… bummer…” from his class. But he insisted, “How about possible?”

Yea! How about possible? – Gosh, I cannot just imagine if I had wits just like the scriptwriter of this movie. Brilliant isn’t she? Her words are well-dedicated. Why the scriptwriter? Because I learned from somebody that films doesn’t look appealing to watch (just) because of the directors, but it (also) do look excellent because of the words, delightful words from scriptwriters.

Anyways, let’s go back to the story. Ü Yea, it is really possible to change our world. We still have a chance, if we still have a hope. But changing doesn’t stop to (just) hoping. You want to change a thing because you were holding on to something, or somebody believed that you can.

Changing always starts/refers on what somebody’s thinking and tries to place it into action. That’s what an eleven year old, Trevor McKinney did. Out of curiosity, he tried and thinks of something a child like him could do that special thing. And there’s a time that he wants to give up because he thinks that “Pay It Forward” didn’t work. But it did work.

He (Trevor) started with a man in a junk namely, Jerry. Oh, I really don’t know what he did to that man. What words did he tell to him or how did he help him. Jerry has a messed up life, and Trevor gave him a chance to live and fixed it. He gave him money to buy clothes and shoes to get a job.

Getting along with the story, Jerry thought that he can’t achieve what he has to pay forward until he saw a woman who wants to commit suicide. Then he changed his thinking. “Cause I owe somebody a favor…” that’s his reason why he help that woman. But no, he helped the woman not because he have to or owe somebody a favor, but he helped the woman because he knows that’s the right thing to do. And he believes that helping is a way his life would be saved.

A messed up life changed into something new. Someone visualized his new saved life and turned back home. And to thank that person who saved him from drowning, he followed what that person wants to, pay it forward. He pursued it not because it must be done. He pursues paying it forward because he also thinks that it is possible to change the world.

“What did you ever do to change the world?” – Trevor to Mr. Simonet. Oh yes, what did I/can I ever do to change the world? Quite ironic… but I must tell myself to think. Think of, as a teenager, an individual, what thing can I contribute to change our world? Before I die, could I have done something that I could be proud of?

The Prince of Egypt

http://www.youtube.com/watch?v=Gur8ccqrQ9c

Many times I had watched this movie; I can still remember the original chronicle. This doesn’t make me forget how Moses accepted the responsibilities, God had given him. This was really my all time favorite story (the story of Moses) in the Bible. That I came to buy a book entitled, “My Book of Bible Stories”, when I was a young kid.

Though there are some reversed characters, and the director or the story writer inserted some scenes (that was not written in the Bible) in the movie, the whole story was still provided with pure moral lessons on how to follow the laws, especially the Laws of God.

First, is to protect not only yourself but your sons, daughters, brothers, sisters, parents, and everyone else around you. Protecting one’s life is more to like ‘protecting Father’s child’. In the (real) family of Moses, Yocheved (mother), Aaron (brother), Miriam (sister), they did every possible way to save his life from Pharaoh, who ordered to kill the new born babies. And because he was saved from the hindrances along the river, they believed that he’s the “deliver” of God.

One of us, especially babies, is a ‘deliver’ of God (that’s why they were called blessing). So, we must be a shelter to protect and defend each individual; not just because of a thing or so, but to think that s/he is a Father’s child, our brother.

Second, is being a brother… I don’t truly believe that being a brother or a sister to someone is just by blood; because such people treat others like their own siblings, especially to friendship. Like in the movie, Rameses and Moses were not brothers by blood, but since Rameses got attached to Moses and had that bond of friendship that’s more to like brothers, he doesn’t mind at all and never allow himself to think of losing Moses for his own royalty – and that is acceptance of someone.

“All I’d ever known to be true is a lie…” (Moses) – This line really broke my heart. Who would ever think of accepting a lie through your life is simple? May I say, “The truth hurts, but lies worse”. And those words, “I understand what you feel,” I say, “No!” Because you really don’t until you experience it and happens that you encountered. But no matter how difficult it is, just to live your life better and achieve great happiness, acceptance is always the key to every flaw; and if there’s acceptance, of course, you also have to forgive.

In my own belief, each man’s purpose why he’s still breathing is to be happy. But we’re not only living just for ourselves; but for the others. If God can forgive seven times, why can’t we that are simply human made through his own flesh? – And how can we achieve pure happiness on our own if forgiving someone on something seems hard for us to do?

Lastly, is to believe. Believe in Him. He has the knowledge of everything you and everyone around you, don’t understand. He’s done writing your whole life story before you do wish for a better one. It’s just your decision if you’re going to choose his lighten path or the other way around. He’s our guide; and having faith in Him means protecting and loving your life. Don’t lose hope to anything. He’s got a better plan.

As I watch the movie, and to compare the Laws of Man to Laws of God: in the Laws of Man, poor people were considered slaves, and wealthy one, or let me say “royal blood”, people bowed down to them as they were their ascendant. While to Laws of God, neither you’re wealthy nor unfortunate; if you’re a creature, you’re first duty as individual is to respect everyone! – “Thou shalt love thy neighbor as thyself.”

And taking His place? – People must know the first great commandment: “Thou shalt love the Lord thy God with thy whole heart, and with thy whole soul, and with thy whole mind, and with thy whole strength”, is (for me) equivalent to the first commandment: “You shall have no other gods before Me”, in my own opinion, this is the most and very important. He’s everything! He’s the Lord of all creatures.

See You Soon, Sweet Prince... (AJ Perez tribute)

Late Upload. - Another video tribute for the late young actor Antonello Joseph "AJ" Sarte-Perez. I made this second video for your requests. I hope you guys can still watch it. Thank You.

February 17, 1993 - April 17, 2011

You will... and FOREVER BE LOVED. (AJ PEREZ tribute)

Part One.

Part Two.

Late upload. - This video tribute is for the late young actor, Antonello Joseph "AJ" Sarte-Perez, who died last April 17, 2011.

On April 17, 2011, Perez had just finished a show in Dagupan and was riding an ABS-CBN service van on his way home with his father Gerardo, and four others. The driver of the van tried to overtake a trailer truck but collided with a Partas provincial passenger bus along MacArthur Highway in Barangay San Julian, Paniqui, Tarlac. He was declared dead on arrival at the Rayos-Valentin Hospital in Moncada, Tarlac at 12:10 a.m. Initial reports said that the cause of his death is "multiple head injuries". The autopsy, however, revealed that his broken ribs pierced his heart and lungs thus causing his death. (http://en.wikipedia.org/wiki/AJ_Perez)


February 17, 1993 - April 17, 2011

Nang N I L I S A N ` M O .

Masakit mawalan… iwanan.

Ano pa nga bang mas sasakit kung ang taong mahal at isa sa mga importante sa buhay mo ay lisanin ang mundong dati’y magkasama niyong ginagalawan? Sa simula’y mahirap tanggapin. Kailan ba naman kasi naging madali ang isiping ‘Wala na siya’, o di kaya’y ‘Bukas, hindi ko na siya makikita o masisilayan’?

“Diba Pa, ‘pag mabait ka, mahal ka ng Diyos? Tsaka diba, ‘pag mahal mo ang isang tao hindi mo sasaktan? Hindi mo sinasaktan ang minamahal mo. Eh bakit tayo, sobra Niya tayong sinusubukan?” (-- Ms. Ai-ai de las Alas in Maalaala Mo Kaya Episode, “Krus”). Ang sabi nga nila, “Kapag nagmamahal tayo, nasasaktan tayo.

Halos lahat sa mga nakikita nating naiiwanan ay ang mga magulang. Kasi simula palang, sila naman na talaga ang laging nandyan. Bihira lang na ang anak ang iniiwanan. Nakikita natin ang paghihirap nila at ang paglaban sa sakit ng paglisan ng mahal sa buhay para sa natitira pa. Hinihiling nila sa Kanya ang KATATAGAN para mapanumbalik ang dating sigla at buhay. Kasi, hindi pa nga naman natatapos ang buhay nila kapag may nawala.

Friendship, couple, pair, partner, pero anong tawag kapag nag-iisa ka nalang? Karamihan sa mga lumilisan, may asawa. Minsan, kasi matanda na. Dahil sa edad, kaya hindi na kinaya. Naiintindihan na natin ‘yun. Halos bihira lang naman sa mag-asawa ang maghiwalay ng mundo na aksidente ang dahilan. (Yung happily married huh.)

Ang swerte nila noh? Kasi, sa mga natitirang araw at panahong nailagi ng isa, nakasama niya ang naging kalahati at kabiyak ng puso at buhay niya. They spoke to their vows, “… from this day forward, for better, for worse, for richer, for poorer, in sickness and in health, until death do us part.” At sila ang nakakaalam at makakapagsabi, kung paano nila naisakatuparan ang mga pangakong ito sa harap ng Panginoon at sa mga saksi sa araw na iyon.

Pero paano naman ang mga magkasintahan? Na kung iisipin, kulang ang isang araw sa tuwing magkasama. Paano natin sila maiintindihan kapag sila na ang nawalan? Paano natin papakinggan ang pagdaing nila sa pagkawala ng isa? Paano natin susubukang maramdaman ang pagkamatay ng kalahati ng puso nila? Paano silang nagsisimula nang buuhin ang pangarap at naghihintay ng magandang bukas sa piling at bisig ng bawat isa? Alam nga ba natin ang sakit na pinagdaraanan at nilalabanan nila?

Minsan sa buhay, may mga bagay na kailangang pagsinungalingan. May mga salitang, mas mabuting hanggang doon na lamang. Kung minsan kasi, doon tayo mas nagiging panatag.

Malimit nating sinasabi sa taong nawawalan ng mahal sa buhay, “Kaya mo ‘yan… NAIINTINDIHAN KITA!” Pero, hindi naman talaga ‘di ba? Dahil hindi naman ikaw o tayo ang nasa posisyon nila para maramdaman iyon. Pwera nalang siguro kung napagdaanan na natin. ‘Dun, maniniwala pa akong naiintindihan mo nga siya. Pero kung hindi, maiintindihan kayang talaga natin?

“I want to be a teacher, a lawyer, and suddenly a doctor. I want to be able to write well, to sing well, and to dance well. All of those changed except one. I knew I want to marry a guy. And his name was AJ Perez…” – The sweetest thing I’ve ever heard.

 “… He told me that even if I don’t say ‘I love you’ back away or show him sweetness just like he would, his exact words were, ‘I would wait a lifetime.’…” – He’s starting to fulfill his promise.

“… If this is God’s way of showing me forever, I accept it…” – Ang mahalin ang taong minsang naging mundo niya habang buhay.

“… AJ taught me how to love. He was very selfless. His love was the most pure thing on Earth. It was, in every way, unconditional. And probably that’s the message here. He wants all of us to love the way he did also.” – And he made us feel, the love of God.

– Steph Ayson, AJ Perez’s girlfriend, eulogy for him.

Isang tanong para sa kanila (mga naiwan), “Kailan niyo kayang magmahal muli nang hindi na ulit matatakot na muling masaktan at lumuha?” At sa mga susubukang buksan ang natitira pang bahagi ng puso nila, “Hanggang kailan kayo maghihintay at uunawain ang bawat patak ng luha nila?” – dahil sabi nga ng ila, mahirap makipagkumpitensya sa patay.

Ang bawat isa’y makasalanan. Dahil hindi naman lahat ay pawang katotohanan. Mula sa pagmulat, hanggang sa pagpikit muli ng mga mata, may mga bagay nang hindi mo nais maranasan. May mga pagkakamali ka na minsa’y hindi kailangang pagsisihan.

Tulad nalang ng pagNGITI. Sa dami mong problema, iiyak ka pa ba? Hindi ba’t mas mabuting ngumiti ka nalang? Hindi ka pa mag-iisip kung anong pwedeng sabihin at idahilan kung sakaling magtanong sila, “Okay ka lang… may problema ba?” Kung sasagot ka naman, “Okay lang ako, wala naman akong problema.” Naku, nakapagsinungaling ka pa.

Ang hirap talaga pag isang ngiti ang ibinigay sa iyo ng isang tao. Dahil sa ISANG bagay na iyon, isang libong kahulugan na ang naroon.

Mahirap ngumiti, tumawa, o ang magpakasaya lalo kung alam mo sa sariling sa pagngiti mong iyon, isang matamis na kahapon at isang realidad ng ngayon na hindi na tulad noon ang kasiyahan mong higit na hindi kayang pagsinungalingan.

“It’s never the tears that I used to measure my pain. Sometimes, it’s the smile that I fake just to show others I’m okay.”