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Thursday, March 7, 2013

Determining the Distance between Lightning and an Observer

We can actually measure the distance between the location of lightning and an observer according to his observation. Let's illustrate that by treating the question in a book by Paul Hewitt.

What is the approximate distance of a thunderstorm when you note a 3-s delay between the flash of lightning and the sound of thunder? 

To make things easier, let's assume that the speed of light is 300,000,000 m/s and that the speed of sound is about 340 m/s (speed of sound in air at 20 deg Celsius). Indeed, light travels faster than sound. Consequently, when light and sound came from the same source, light arrives to a certain destination first.

Variables and Relationships
Let
$latex \displaystyle t_{L}$ be the time for light to travel the distance between the origin of lighning and you.
and
$latex \displaystyle t_{S}$ be the time for sound to travel the same distance.
From the question, 3-s delay between the flash of lightning and the sound of thunder, we can translate this into a mathematical equation. 
$latex \displaystyle t_{S}=t_{L}+ 3 \textup{ s} \longrightarrow (\textup{Eq.} 1) $ 
Let's call this as Eq. 1.
Both travel at constant speeds. So, the relationship among the speed, distance travelled and time can be expressed mathematically as
$latex v_{S}=\frac{d}{t_{S}} \longrightarrow (\textup{Eq.} 2) $
$latex v_{L}=\frac{d}{t_{L}} \longrightarrow (\textup{Eq.} 3) $
Solution
We substitute the expressions for the times described by Eq. 2 and Eq. 3 into Eq. 1 and we'll have.
$latex \frac{d}{v_{S}} = \frac{d}{v_{L}} + 3 \textup{ s} $
Now, we have one equation with only one unknown, that is, d. 
$latex \frac{d}{v_{S}} - \frac{d}{v_{L}} = 3 \textup{ s} $
$latex d \Bigg (\frac{1}{v_{S}} - \frac{1}{v_{L}} \Bigg) = 3 \textup{ s} $
$latex d = \frac {3 \textup{ s}}{\cfrac{1}{v_{S}} - \cfrac{1}{v_{L}} }$
$latex d = \frac {3 \textup{ s}}{\cfrac{1}{340 \textup{ m/s}} - \cfrac{1}{300,000,000 \textup{ m/s}} }$
$latex d = 1,020 \textup{ m } $
And that's the distance we're looking for. Well, this is just an estimate. Here we've rounded off the value of speed of light. In reality it's not really exactly 300,000,000 m/s. Also, the sound may not really be 340 m/s but may depend on the temperature of the air in the surrounding. But anyway, the important thing here is the process in solving the question and not the values. :-)

Sunday, March 3, 2013

Sabah Standoff and Sultan Kiram III

Map showing Sabah and Southern part of Philippines
To many Muslims of southern Philippines, Sabah is the nearest refuge to escape poverty and hard life in Philippines. Though, many of them have entered it by wearing the unwanted label as "illegal aliens," they have managed to flourish there or, if not, experience the good ambiance of good governance and economic stability of the place, to say the least, since Sabah has prospered under Malaysia.

A little dig on the history of this issue, Sabah was given to the Sultanate of Sulu as a gift and then eventually became once loosely worded contract to a British trading company that paved the way for it to be part of Malaysian territory.

The contract between Sri Paduka Maulana Al Sultan Mohammad Jamalul Alam, representing the sultanate as owner and sovereign of Sabah on one hand, and that of Gustavus Baron de Overbeck and Alfred Dent representing the North Borneo Company, on the other, as lessees of Sabah, was executed on January 22, 1878.
Sultan Jamalul Kiram III
That Lease prohibits the transfer of Sabah to any nation, company or individual without the consent of the Government of the Sultan of Sulu. 
Less than a decade later, the Sultanate of Sulu came under the control of Spain and was forced to sign a document giving all of the Sultan’s Properties in Palawan and Sulu (excluding Northern Borneo) to Spain. In 1885, Spain relinquished all of its claim to Borneo to the British in the Madrid Protocol of 1885.

President Aquino
The sudden move of Sultan Jamalul Kiram III this early February puts this topic into spotlight again. Royal Army of Sulu wants Malaysia to recognise it as the rightful owner of Sabah, and to renegotiate the terms of the old lease - something Malaysia has made clear it has no intention of doing. 

But by creating havoc in Sabah in order to put a pressure on Malaysia and Philippine governments for them to resolve this issue, I think that was where the Sultan fell short. Indeed, he might have a better plan other than this one. Back in 2010, he even wrote a letter to President Aquino for this but sadly,it was snubbed by the Malacanang palace. 

One big question we might ask now is: Why is President Aquino turning a deaf ear towards Sultan? Is President Aquino coward enough to loose hope in the Sabah claim?
Norberto Gonzales

In one angle, foremost many Filipinos have been reaping the peaceful and rich economy of Malaysia. To support Sultan's action means to jeopardize the lives of those many. Just to today, at least 289 Filipinos arrived at Zamboanga city from Sabah after they were deported by Malaysian authorities. And siding Sultan Kiram would be taken by Malaysia as a provocative act into invasion. And Philippine military is not that strong enough to pose a sufficient threat if the only way to resolve it comes to one single final resort - war (whether we like that word or not). From reports in 2012, junks of military equipment were donated by US to Philippines. So, to put that card on the table is a suicide. 


ex-president Arroyo
And from another seemingly strange perspective, Malacanang believes that this action of Sultan is a piece of masterpiece drafted by an intelligent. They suspect the national security adviser of ex-president Gloria Arroyo, Norberto Gonzales, as behind this sabotage. Like in 2001, when Misuari staged a rebellion, Gonzales was known to have exerted influence to allow the former governor of Autonomous Region in Muslim Mindanao (ARMM) to be placed under house arrest. Thinking that the sultan was in the senatorial ticket of the Arroyo administration in 2007, could the ex-president be far behind? If this were to be true, it'd be heartbreaking to witness in this modern age another sultan becoming a victim of deception, just as what happened in the past - the power of Sultanate of Sulu have massively faded because of deception of the West.

It's hard to swallow but it would have been best if Sultan stayed in Sulu and established peaceful and strong ground before even thinking of going into Sabah to complain about the rent. His men would not have lost their lives over the battle against the strong army of Malaysia.

Even if he could succeed in claiming Sabah totally, his other fellow muslims may still opt Sabah to be part of Malaysia rather than Sabah under a christian country.

What is certain right now is that the real enemies of Islam are rejoicing while sitting on couch and watching muslims killing one another! Indeed, they have succeeded once again.

So, what is your say on this?

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