Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main2018MathematicsHeights and DistancesActual

A man on the top of a vertical tower observes a car moving at a uniform speed towards the tower on a horizontal road. If it takes 18 min for the angle of depression of the car to change from 30 ° to 45 ° , then the time taken (in min ) by the car to reach the foot of the tower is

Options

  1. A9 2 3 - 1
  2. B18 1 + 3
  3. C18 3 - 1
  4. D9 1 + 3

Correct answer

D. 9 1 + 3

Step-by-step solution

Let length of tower be h . ⇒ A C ′ = A B = h And A C = A B cot 30 ° = 3 h ⇒ C C ′ = 3 - 1 h Time taken by car form C C ' = 18   min ⇒ Time take by car to reach the foot of the tower = 18 3 - 1   min = 9 3 + 1   min

Practice Heights and Distances on Quantrex Academy →

More from Heights and Distances

The angle of elevation of the top P of a tower from the feet of one person standing due south of the tower is 45 ° and from the feet of another person standing due west of the 2023From the top A of a vertical wall A B of height 30 m , the angles of depression of the top P and bottom Q of a vertical tower P Q are 15 ∘ and 60 ∘ respectively, B and 2023The angle of elevation of the top of a tower from a point A due north of it is α and from a point B at a distance of 9 units due west of A is cos - 1 3 13 . If the distance of 2022A horizontal park is in the shape of a triangle O A B with A B = 16 . A vertical lamp post O P is erected at the point O such that ∠ P A O = ∠ P B O = 15 ° and &#8 2022The angle of elevation of the top P of a vertical tower P Q of height 10 from a point A on the horizontal ground is 45 ° . Let R be a point on A Q and from a point B , vertica 2022Let a vertical tower A B of height 2 h stands on a horizontal ground. Let from a point P on the ground a man can see upto height h of the tower with an angle of elevation 2 α 2022A tower P Q stands on a horizontal ground with base Q on the ground. The point R divides the tower in two parts such that Q R = 15 m . If from a point A on the ground the angle of 2022From the base of a pole of height 20 meter, the angle of elevation of the top of a tower is 60 ° . The pole subtends an angle 30 ° at the top of the tower. Then the heigh 2022 Full Heights and Distances list All JEE Main PYQs