A man is observing, from the top of a tower, a boat speeding towards the tower from a certain point A, with uniform speed. At that point, angle of depression of the boat with the man’s eye is 30° (Ignore man’s height). After sailing for 20 seconds, towards the base of the tower (which is the level of water), the boat has reached a point B, where the angel of depression is 45°. Then the time taken (in second) by the boat from B to reach the base of the tower is:

Ask & Answer Question

Ncert Solutions Maths class 11th Maths Class 11th

A man is observing, from the top of a tower, a boat speeding towards the tower from a certain point A, with uniform speed. At that point, angle of depression of the boat with the man’s eye is 30° (Ignore man’s height). After sailing for 20 seconds, towards the base of the tower (which is the level of water), the boat has reached a point B, where the angel of depression is 45°. Then the time taken (in second) by the boat from B to reach the base of the tower is:

Option 1 -

$10 (\sqrt[]{3} - 1)$

Option 2 -

$10 (\sqrt[]{3} + 1)$

Option 3 -

Option 4 -

$10 \sqrt[]{3}$

2 Views | Posted a month ago

Asked by Shiksha User

1 Answer

Answered by

alok kumar singh | Contributor-Level 10

a month ago

Correct Option - 2

Detailed Solution:

$∴ I n Δ A Q P$

$t a n 30 ° = \frac{P Q}{A Q}$ $\frac{1}{\sqrt[]{3}} = \frac{h}{x + y}$

x + y = $\sqrt[]{3} h . . . . . (i)$

$∴ l n Δ B Q P$

$t a n 45 ° = \frac{h}{y}$

h = y .(ii)

(i) & (ii) x + y = $\sqrt[]{3} y$

$\Rightarrow x = (\sqrt[]{3} - 1) y . . . . . . . (i i i)$

Let the speed be S

$\frac{x}{S} = 20$

x = 20.S

from (iii)

$\frac{y}{S} = 10 (\sqrt[]{3} + 1)$

<math> <mrow> <mo>∴</mo> <mi>I</mi> <mi>n</mi> <mtext> </mtext> <mtext> </mtext> <mi>Δ</mi> <mi>A</mi> <mi>Q</mi> <mi>P</mi> </mrow> </math>          <math> <mrow> <mi>t</mi> <mi>a</mi> <mi>n</mi> <mn>3</mn> <mn>0</mn> <mo>°</mo> <mo>=</mo> <mfrac> <mrow> <mi>P</mi> <mi>Q</mi> </mrow> <mrow> <mi>A</mi> <mi>Q</mi> </mrow> </mfrac> </mrow> </math> <math> <mrow> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mroot> <mrow> <mn>3</mn> </mrow> <mrow></mrow> </mroot> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mi>h</mi> </mrow> <mrow> <mi>x</mi> <mo>+</mo> <mi>y</mi> </mrow> </mfrac> </mrow> </math>        x + y = <math> <mrow> <mroot> <mrow> <mn>3</mn> </mrow> <mrow></mrow> </mroot> <mi>h</mi> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mrow> <mo>(</mo> <mrow> <mi>i</mi> </mrow> <mo>)</mo> </mrow> </mrow> </math>   <math> <mrow> <mo>∴</mo> <mi>l</mi> <mi>n</mi> <mtext> </mtext> <mtext> </mtext> <mi>Δ</mi> <mi>B</mi> <mi>Q</mi> <mi>P</mi> </mrow> </math>           <math> <mrow> <mi>t</mi> <mi>a</mi> <mi>n</mi> <mn>4</mn> <mn>5</mn> <mo>°</mo> <mo>=</mo> <mfrac> <mrow> <mi>h</mi> </mrow> <mrow> <mi>y</mi> </mrow> </mfrac> </mrow> </math>          h = y .(ii)(i) & (ii) x + y = <math> <mrow> <mroot> <mrow> <mn>3</mn> </mrow> <mrow></mrow> </mroot> <mi>y</mi> </mrow> </math>   <math> <mrow> <mo>⇒</mo> <mi>x</mi> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mroot> <mrow> <mn>3</mn> </mrow> <mrow></mrow> </mroot> <mo>−</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> <mi>y</mi> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mrow> <mo>(</mo> <mrow> <mi>i</mi> <mi>i</mi> <mi>i</mi> </mrow> <mo>)</mo> </mrow> </mrow> </math>     Let the speed be S <math> <mrow> <mfrac> <mrow> <mi>x</mi> </mrow> <mrow> <mi>S</mi> </mrow> </mfrac> <mo>=</mo> <mn>2</mn> <mn>0</mn> </mrow> </math> x = 20.Sfrom (iii) <math> <mrow> <mfrac> <mrow> <mi>y</mi> </mrow> <mrow> <mi>S</mi> </mrow> </mfrac> <mo>=</mo> <mn>1</mn> <mn>0</mn> <mrow> <mo>(</mo> <mrow> <mroot> <mrow> <mn>3</mn> </mrow> <mrow></mrow> </mroot> <mo>+</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mrow> </math>

0 Upvotes 0 Downvotes

Get authentic answers from experts, students and alumni that you won't find anywhere else

On Shiksha, get access to

65k Colleges
1.2k Exams
688k Reviews
1800k Answers

Community GuidelinesUser Points System

QuestionsDiscussionsTags

1 Answer

Learn more about...

Most viewed information

Share Your College Life Experience

Didn't find the answer you were looking for?

Need guidance on career and education? Ask our experts

Your Question