Problems Involving Shadows


 
 
Concept Explanation
 

Problems Involving Shadows

A shadow is a dark area where light from a light source is blocked by an opaque object. It occupies all of the three-dimensional volume behind an object with light in front of it. The cross section of a shadow is a two-dimensional silhouette, or a reverse projection of the object blocking the light.

Problems Involving Shadows : Shadows are formed when the person is obstructing the path of light. In the morning as the Sun rises from the East.

  •  If a person facing towards Sun that is East, the shadow will be towards his back or in West.
  • If a person facing towards South, the shadow will be towards his right. that is West
  • If a person facing towards West, the shadow will be towards his front. or West
  • If a person facing towards North, the shadow will be towards his left which is  West
  • But in the evening as we know the sets in the West. All these directions will be reversed.

  • When two persons facing each other during sunrise, the shadow of both are formed at the left of the person facing north.
  • When two persons facing each other during sunrise, the shadow of both are formed at the right of the person facing south.
  • When two persons facing each other during sunset, the shadow of both are formed at the right of the person facing north.
  • When two persons facing each other during sunset, the shadow of both are formed at the left of the person facing south.
  • Illustration :  In an evening when Suraj started walking from his house, his shadow was exactly towards his right. He walked 6 km. Then he turns to his left and moved 4 km. Again he turns to his right and walked 6 km. Then he turns to his right and moved 13 km. How far is he and in which direction from the starting point ?

    A. 15 km North-East          B. 15 km North              C.  15 km South-East              D.  16 km South             E. 17 km East 

    Answer : A

    Solution : In the evening when the Sun is in the West the shadow is in East In an evening when Suraj started walking from his house, his shadow was exactly towards his right. that means he is facing in North Direction.

  • Then He reaches point B after traversing a distance of 6 Km
  • Then he turns to his left and moved 4 km and reaches point C.
  • Again he turns to his right and walked 6 km and reaches point D
  • Then he turns to his right and moved 13 km and reaches point E
  • The path he has traversed is shown in the figure below

     

    The distance between A and E is calculated using pythagoras theorem

    We see that Delta AFE is a right angled triangle, right angled at F. So AE is the hypotenuse as it is the side opposite to right angle.

    AF= AB + CD = 6 + 6 = 12; km

    FE = DE - BC = 13 - 4 = 9 km

    EA = sqrt {AF^2+EF^2}=sqrt {12^2+9^2}

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    Sample Questions
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    Question : 1

    Darpan is living from office and reaches his home at 5:30 PM, he knocked his door and waits to open it, his shadow was formed in his right.  In which direction he is facing now?

    Right Option : C
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    Question : 2

    One morning, after sunrise, Vikram and Shailesh were standing in a lawn with their backs towards each other. Vikram's shadow fell exactly towards left hand side. Which direction was Shailesh facing?

    Right Option : D
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    Question : 3

    One evening before sunset two friends Sumit and Mohit were talking to each other face to face. If Mohit's shadow was exactly to his right side, which direction was Sumit facing?

    Right Option : D
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