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QJEEM21Ma2e72: JEE Main 2021 Mathematics - Class 12 JEEM21Ma2e72 Solution: A man is observing, from the top of a tower, a boat speeding…

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

Multiple Choice Options

  • A 10(3+1)10(\sqrt 3 + 1)
  • B 10(3−1)10(\sqrt 3 - 1)
  • C 10
  • D 10310\sqrt 3

Step-by-Step Verified Solution

JEE Main 2021 (Online) 25th February Morning Shift Mathematics - Height and Distance Question 17 English Explanation
hx+y=tan⁡30∘{h \over {x + y}} = \tan 30^\circ

x+y=3hx + y = \sqrt 3 h ...... (1)

Also,

hy=tan⁡45∘{h \over y} = \tan 45^\circ

h=yh = y ..... (2)

put in (1)

x+y=3yx + y = \sqrt 3 y

x=(3−1)yx = \left( {\sqrt 3 - 1} \right)y

x20=′v′{x \over {20}} = 'v' speed

∴\therefore time taken to reach Foot from B

=yV= {y \over V}

=x(3−1).x×20= {x \over {\left( {\sqrt 3 - 1} \right).x}} \times 20

=10(3+1)= 10\left( {\sqrt 3 + 1} \right)

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