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Suppose you are standing in a field near a straight section of railroad tracks just as the locomotive of a train passes the point nearest to​ you, which is 1/5 mi away. The​ train, with length 1/12 mi, is traveling at 13 mi/hr. If you start running in a straight line across the​ field, how slowly can you run and still catch the​ train? In which direction should you​ run? Let v be your velocity and let x be the difference between the position of the locomotive when it passes you and the position at which you catch the tail of the train. What is the objective function in terms of​ x?

Question
Suppose you are standing in a field near a straight section of railroad tracks just as the locomotive of a train passes the point nearest to​ you, which is 1/5 mi away. The​ train, with length 1/12 mi, is traveling at 13 mi/hr. If you start running in a straight line across the​ field, how slowly can you run and still catch the​ train? In which direction should you​ run?
 
Let v be your velocity and let x be the difference between the position of the locomotive when it passes you and the position at which you catch the tail of the train. What is the objective function in terms of​ x?
check_circleAnswer
Step 1

As a first step, let's convert the given information in a diagram. Please see the white board.

Let A be the point where you are standing. Let B be the position of the locomotive when it passes you and C be the position at which you catch the tail of the train. CD = length of the train.

C
X
A
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C X A

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Step 2

Note that triangle ABC is a right angled triangle. AB = 1/5; BC = x

Please see the white board.

1
1
2
x
АС - АВ" + Вс?
52
25
1
25
— АС -
x
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Image Transcriptionclose

1 1 2 x АС - АВ" + Вс? 52 25 1 25 — АС - x

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Step 3

Time taken by the train to cover BD = Time taken by you to cover AC

Hence, BD / sp...

1
+x
12 V25
1
13
1
13x
'V 25
1
(x
12
help_outline

Image Transcriptionclose

1 +x 12 V25 1 13 1 13x 'V 25 1 (x 12

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Math

Calculus

Functions

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