Gridiron physics: Scalars and vectors - Michelle Buchanan

烤架物理學:路徑長與向量 - 米歇爾·布坎南

Transcriber: Andrea McDonough Reviewer: Bedirhan Cinar

譯者: 瑞文Eleven 林Lim 審譯者: XiuDe Huang

Fourth and nineteen, folks,

現在是4:19了，各位

they've gotta have a play as time's ticking away

他們要在時間流逝時打場精彩的比賽

because they've got to stay in this ball game,

因為他們要留在比賽中

they've got to win.

他們一定要贏

They come out lined up in the empty set,

他們在中線上排一直線

three receivers to the right,

三個接球員到右邊

two to the left.

兩個到左邊

Defense looks like they're gonna to man up with no safety.

防守方似乎不會讓他們安全通過

This is the exact offensive match-up that they want:

這完全是他們要的攻勢

the best receiver lined up against the linebacker.

最好的球員在中線對上後衛球員

Quarterback steps back to receive the ball,

四分衛往後退5碼接球

five yards deep in the gun.

向槍一樣上膛

He takes a snap, drops three steps,

他拿到發球，往後退三步

he plants his back foot,

他計畫從後面傳球

he's looking for an opening.

他正在找一個無人防守的隊友

There's a blitz coming off the edge!

他們從左側使出了 閃電突擊(美式足球用語)

He steps up to avoid the rush.

他往前站躲過突擊

He's looking down field.

他看往前方

He's got the inside receiver making a cut.

他看到一個接球員切過中場

He's got a step on the linebacker.

那個球員跑到了後衛球員旁

Quarterback has a beat on it.

敵方的四分衛準備要撂倒他

He lets the ball go,

我方的四分衛把球拋向遠方

it's in the air!

球正在空中

Receiver is out in front of the defender.

接球員超過了防守方

He's got it beat!

他衝去接住球

He's out in front, racing for the ball!

他在前方，為了球奮力跑著

It's coming down!

球要來了

He cradles it at the fifteen!

他在15碼接住了球

He's at the ten, five!

他現在在10，5

Touchdown!

達陣

Unbelievable play!

真是一場令人難以置信的比賽

Now, wait a minute.

現在，等一下

Of course, it's believable,

當然，這是可以相信的

it's physics,

這是物理

specifically the differences between scalars and vectors.

特別是路徑長和向量之間的差別

So, let's just see that replay.

所以，讓我們重播一次

"Quarterback steps back to receive the ball,

四分衛往後退5碼接球

five yards deep in the gun."

向槍一樣上膛

Stop.

暫停

See, measurements are defined as two different quantities.

看，一個測量通常是由兩個元素組成

Scalars are measurements with only numbers,

純量只有數字

and vectors are measurements with direction.

向量則還包含了方向

For example, when that quarterback takes the snap,

例如，當四分衛退到後方

he's five yards away, but from where?

他退了五碼，但是從哪裡?

Back from the line of scrimmage,

從主場的中線，

so the five yards by itself is a scalar quantity.

所以他自己移動五碼是路徑長

When you add a direction,

當你把方向加進去

like five yards deep,

像往後五碼

it becomes a vector quantity.

這就變成了向量

Five yards - scalar,

五碼---純量

five yards deep - vector.

往後五碼---向量

OK, go ahead.

好，讓我們繼續吧

"He takes a snap, drops three steps.

他拿到球，往後退三步

He plants his back foot, he's looking for an opening.

他計畫從後面傳球 他正在找一個無人防守的隊友

There's a blitz coming off the edge!

他們從左側使出了閃電突擊

He steps up to avoid the rush."

他往前站躲過突擊

Whoa!

哇!

Here's a difference between distance and displacement.

這裡有個路徑長和位移的差異

Distance is a measurement

路徑長呢

without identifying where you moved.

沒有定義你向哪裡移動

It's a scalar quantity.

他是個純量

When the quarterback makes a three-step drop,

當四分衛往後退三步

he moves about three yards back.

他大概移動了三碼

When he moves about another three yards forward,

當他又往前三碼

when he steps up into the pocket,

進到球員圍成的圈時

so that quarterback moves a total distance of six yards.

四分衛總共移動了六碼

That's a distance, that's a scalar.

那就是路徑長，也是純量

Now, displacement is a vector quantity,

現在，位移則是向量

describing about how far out of place the object is.

描述一個物體對於同一個位置

移動了多遠

So the quarterback dropped back three yards

所以他往後退三碼

and then moved back forward three yards,

然後又往前三碼

he's in the exact same place where he started.

他回到開始的地方

So, his displacement is zero yards.

所以他的位移是零

Distance - six yards,

路徑長---六碼

displacement - zero yards.

位移---零碼

So, let's look at what happened next.

讓我們繼續往下看

"Quarterback has a beat on it, he let's the ball go!

敵方的四分衛準備要擊倒他

我方的四分衛把球拋向遠方

It's in the air!

球正在空中

Receiver is out in front of the defender."

接球員超過了防守方

Stop.

停

So, here's speed and velocity,

接著，速率和速度出現了

but let's just do one thing at a time.

但讓我們一個一個來

So, speed is measurement without direction,

速率是沒有方向的量

it's a scalar quantity.

它正是純量

Velocity is a vector quantity.

而速度則是向量

It is that object's speed,

這是那個物體的速率

but with a direction of motion.

但是有方向

So the receiver accelerates away,

所以，接球員正在加速

gaining both speed and distance.

速度和距離同時產生

This takes the receiver 5 seconds to run those 50 yards.

接球員總共花了五秒

跑了五十碼

So his average speed, in any given time,

所以他的平均速度，在任何一個時間

is 10 yards/second.

都是每秒十碼

The linebacker tries to keep up,

後衛球員想要跟上

but his overall speed is slower,

但他的速率比較慢

he only goes 35 yards in those 5 seconds,

他在五秒內只跑了三十五碼

so his average speed is only 7 yards/second.

所以他的平均速率是每秒七碼

They're both traveling in a forward direction,

他們都往前移動

so their velocity is also positive.

所以他們的向量都是正的

You can't go from resting to your peak speed immediately.

你無法一瞬間就達到最高速度

You've got to build up to it.

你必須慢慢把速度增加

This is acceleration.

這就是加速度

At first the linebacker can keep up with that receiver,

後衛球員一開始能跟上接球員

but eventually the faster receiver pulls away.

但較快的接球員把距離拉遠

That's acceleration, the change in speed over time.

那是加速度，在一定時間內的速度改變

Acceleration is a vector quantity.

加速度是向量的一種

It describes a rate at which an object changes velocity.

它描述一個物體速度的改變

Like velocity, acceleration is a vector.

像速度，他是向量

It happens in a direction.

它在方向中發生

So let's just look at that play just one more time.

所以，讓我們再看一次

"Quarterback steps back to receive the ball,

"四分衛往後5碼接球

five yards deep in the gun."

向槍一樣上膛

Vector!

向量

"He takes a snap, drops three steps,

"他拿到發球，往後退三步

he plants his back foot.

他計畫從後面傳球

He's looking for an opening.

他正在找一個無人防守的隊友

There's a blitz coming off the edge!

他們從左側使出了閃電突擊

He steps up to avoid the rush."

他往前站躲過突擊

Displacement!

位移

"He's got the inside receiver making a cut.

他看到一個接球員切過中場

He's got a step on the linebacker.

那個球員跑到了後衛球員旁

The quarterback has a beat on it.

敵方的四分衛準備要撂倒他

He let's the ball go!

It's in the air!

我方的四分衛把球拋向遠方

球正在空中

Receiver is out in front of the defender!"

接球員超過了防守方

Velocity!

速度

"He's got it beat!

他衝去接住球

He's out in front, racing for the ball!

他在前方，為了球奮力跑著

It's coming down!

球要來了

He cradles it at the fifteen, he's at the ten, five!"

他在15碼接住了球!他現在在10，5

Acceleration!

加速度

"Touchdown! Unbelievable play!

"達陣！真是一場精采的比賽

That was a great play as time expired,

時間流逝時，這真是一場偉大比賽

resulting in the touchdown

達陣造成了最後的獲勝

and ultimately the win and pure effort."

純粹的努力也幫了不少

And pure science.

還有純粹科學