Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

You are not logged in.

## #1 2016-12-27 12:45:09

Mathegocart
Member
Registered: 2012-04-29
Posts: 1,884

### Archer's Arrow Enigma

Hello my purveyors, I have an enigma that is unfortunately perplexing to me...
The archer wants to show his exemplary skill to his friends, so he takes on the challenge of shooting an arrow through the opposing windows of a train that's moving at 120 feet per second. Standing on a platform, the archer shoots. Luckily for him, the arrow reaches the upper right corner of a window(from his vantage point), and the arrow manages to exit through the opposing window's lower left corner(from his vantage point).
Dimensions: The top of the train is 15 ft from the railroad tracks and the tops of each window are 5 ft away from the top of the train. Each window measures 5ft by 24 ft. The (i.e, vertical)perpendicular distance between both opposing windows is 12 ft.
Questions:
If the arrow took 4 seconds to reach the upper right corner of the first window, what were a) the archer's horizontal distance from the train; b) the height of the platform on which he was standing on, if he was standing vertically when he fired the arrow from his shoulder(shoulder height is 5.5 ft). Finally, find c) the time, in seconds, it took for the arrow to hit the ground the moment the arrow left the train(express this in a fraction.)
Neglect all effects of friction, air resistance, drag, and all components of physics that would be problematic. In other words, treat everything as if they were merely points in space, and assume the arrow travelled linearly.

I have perused the problem several times, and it seems to utilize similar triangles and other interesting triangles.( the arrow travels at 65 ft/sec, though my explanation is handwaving.)

I would appreciate a solution from our sagacious members.
-Mathe

The integral of hope is reality.

Offline

## #2 2016-12-27 15:48:40

Mathegocart
Member
Registered: 2012-04-29
Posts: 1,884

### Re: Archer's Arrow Enigma

Is it perplexing to anyone?

The integral of hope is reality.

Offline

## #3 2016-12-27 15:54:36

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Archer's Arrow Enigma

Hi;

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

## #4 2016-12-27 16:19:36

Mathegocart
Member
Registered: 2012-04-29
Posts: 1,884

### Re: Archer's Arrow Enigma

Do you comprehend it?

The integral of hope is reality.

Offline

## #5 2016-12-27 16:21:51

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Archer's Arrow Enigma

Not entirely, as you know physics questions leave me going buh, buh buh...

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

## #6 2016-12-27 17:41:43

Mathegocart
Member
Registered: 2012-04-29
Posts: 1,884

### Re: Archer's Arrow Enigma

Apparently our teacher was so sagacious he could solve this in 10 minutes. I'm utterly confused...

The integral of hope is reality.

Offline

## #7 2016-12-28 01:05:57

Mathegocart
Member
Registered: 2012-04-29
Posts: 1,884

### Re: Archer's Arrow Enigma

Has anyone found a solution or some workings to this bewildering problem?

The integral of hope is reality.

Offline

## #8 2016-12-28 01:18:29

Mathegocart
Member
Registered: 2012-04-29
Posts: 1,884

### Re: Archer's Arrow Enigma

My work is convoluted and bound to baffle my colleagues..

Last edited by Mathegocart (2016-12-28 01:20:04)

The integral of hope is reality.

Offline

## #9 2016-12-28 05:48:29

Mathegocart
Member
Registered: 2012-04-29
Posts: 1,884

### Re: Archer's Arrow Enigma

Perhaps a 3-D model of the enigma would help us appreciably.... I'll get GeoGebra out and model this.

The integral of hope is reality.

Offline

## #10 2016-12-28 07:23:35

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Archer's Arrow Enigma

Hi;

Post #8 looks like art for your freehand drawing class.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

## #11 2016-12-28 08:50:26

Mathegocart
Member
Registered: 2012-04-29
Posts: 1,884

### Re: Archer's Arrow Enigma

bobbym wrote:

Hi;

Post #8 looks like art for your freehand drawing class.

Haha, I abhor art and it is an extremely convoluted drawing.

The integral of hope is reality.

Offline

## #12 2016-12-28 18:17:58

Mathegocart
Member
Registered: 2012-04-29
Posts: 1,884

### Re: Archer's Arrow Enigma

I have solved it... with a bombardment of 3d kinematics and a slew of heinous, ugly algebra.
ew.

The integral of hope is reality.

Offline

## #13 2016-12-28 22:23:05

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Archer's Arrow Enigma

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

## #14 2016-12-29 00:05:54

Member
Registered: 2016-04-16
Posts: 1,086

### Re: Archer's Arrow Enigma

Mathegocart wrote:

The (i.e, vertical)perpendicular distance between both opposing windows is 12 ft.
-Mathe

I like clarity on this point.Is it not horizontal distance between opposing windows?And what is the value of 'g' in fps units? I vaguely remember it as 32 ft/sec^2. Is it right? I am used to S.I. units.

Last edited by thickhead (2016-12-29 00:26:32)

{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

Offline

## #15 2016-12-29 06:55:56

Mathegocart
Member
Registered: 2012-04-29
Posts: 1,884

### Re: Archer's Arrow Enigma

Mathegocart wrote:

The (i.e, vertical)perpendicular distance between both opposing windows is 12 ft.
-Mathe

I like clarity on this point.Is it not horizontal distance between opposing windows?And what is the value of 'g' in fps units? I vaguely remember it as 32 ft/sec^2. Is it right? I am used to S.I. units.

I see that clarity is necessary for answering these questions, it is horizontal distance, the force of gravity is approximately equal to 31 ft/sec^2.

The integral of hope is reality.

Offline

## #16 2016-12-29 20:59:05

Member
Registered: 2016-04-16
Posts: 1,086

### Re: Archer's Arrow Enigma

{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

Offline