The figure above shows the position, at two instants of time, of a 10-meter-long rod as it was falling down to the ground. If one end of the rod was pinned to the ground, by what vertical distance did the rod fall between the two instants of time?a)b)c)d)e)Correct answer is option 'A'. Can you explain this answer?

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The figure above shows the position, at two instants of time, of a 10-meter-long rod as it was falling down to the ground. If one end of the rod was pinned to the ground, by what vertical distance did the rod fall between the two instants of time?

Correct answer is option 'A'. Can you explain this answer?

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The figure above shows the position, at two instants of time, of a 10-...

Given:

Length of rod = 10 meters
Angle with the ground at 1^st instant = 60^o
Angle with the ground at 2^nd instant = 30^o

To find:

Vertical distance covered between the 2 instants

Approach:

We will first try to understand the question
To do so, let us:
- Drop perpendiculars from the free end of the rod at both instants of time
- Label the triangles thus formed

From the diagram, it is clear that we need to find AB – PQ
- (Note: if you are not sure how AB – PQ is equal to the vertical distance covered by the ladder, drop a perpendicular PX on AB. You’ll see that BQPX is a rectangle and so, PQ = BX. So, AB – PQ = AB – BX = AX. The ladder was earlier at a height of A and it is now at a height of X. So, the distance AX clearly denotes the vertical distance covered by the ladder.)

Thus, we need to find AB – PQ
1. AB is a side of right ΔOBA, which is 30-60- 90 Triangle and angle AOB = 60^o
2. PQ is a side of right ΔOQP, which is also a 30-60-90 Triangle with angle POQ = 30^o
In each of the 2 right triangles, we know a side and two angles.
1. So, by using side ratio property of 30-60-90 triangle, we can find the required values

Working Out:

Finding AB
- In right ΔOBA
  - OB: AB: OA = 1: √3: 2
  - We know OA = 10
  - AB: OA = √3: 2
  - Thus AB = 5√3

Finding PQ
- In right ΔOQP
  - PQ: OQ: PO = 1: √3: 2
  - We know PO = 10
  - PQ: PO = 1: 2
  - Thus PQ = 5
Thus, AB – PQ = 5√3 – 5 = 5 (√3 -1) meters
Therefore, the correct answer is Option A.

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Most Upvoted Answer

The figure above shows the position, at two instants of time, of a 10-...

Given:

Length of rod = 10 meters
Angle with the ground at 1^st instant = 60^o
Angle with the ground at 2^nd instant = 30^o

To find:

Vertical distance covered between the 2 instants

Approach:

We will first try to understand the question
To do so, let us:
- Drop perpendiculars from the free end of the rod at both instants of time
- Label the triangles thus formed

From the diagram, it is clear that we need to find AB – PQ
- (Note: if you are not sure how AB – PQ is equal to the vertical distance covered by the ladder, drop a perpendicular PX on AB. You’ll see that BQPX is a rectangle and so, PQ = BX. So, AB – PQ = AB – BX = AX. The ladder was earlier at a height of A and it is now at a height of X. So, the distance AX clearly denotes the vertical distance covered by the ladder.)

Thus, we need to find AB – PQ
1. AB is a side of right ΔOBA, which is 30-60- 90 Triangle and angle AOB = 60^o
2. PQ is a side of right ΔOQP, which is also a 30-60-90 Triangle with angle POQ = 30^o
In each of the 2 right triangles, we know a side and two angles.
1. So, by using side ratio property of 30-60-90 triangle, we can find the required values

Working Out:

Finding AB
- In right ΔOBA
  - OB: AB: OA = 1: √3: 2
  - We know OA = 10
  - AB: OA = √3: 2
  - Thus AB = 5√3

Finding PQ
- In right ΔOQP
  - PQ: OQ: PO = 1: √3: 2
  - We know PO = 10
  - PQ: PO = 1: 2
  - Thus PQ = 5
Thus, AB – PQ = 5√3 – 5 = 5 (√3 -1) meters
Therefore, the correct answer is Option A.

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The figure above shows the position, at two instants of time, of a 10-meter-long rod as it was falling down to the ground. If one end of the rod was pinned to the ground, by what vertical distance did the rod fall between the two instants of time?a)b)c)d)e)Correct answer is option 'A'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about The figure above shows the position, at two instants of time, of a 10-meter-long rod as it was falling down to the ground. If one end of the rod was pinned to the ground, by what vertical distance did the rod fall between the two instants of time?a)b)c)d)e)Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The figure above shows the position, at two instants of time, of a 10-meter-long rod as it was falling down to the ground. If one end of the rod was pinned to the ground, by what vertical distance did the rod fall between the two instants of time?a)b)c)d)e)Correct answer is option 'A'. Can you explain this answer?.

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