Bissoy.com
Doctors Medicines MCQs Q&A

A boat is sailing towards a lighthouse of height 20√3 m at a certain speed. The angle of elevation of the top of the lighthouse changes from 30° to 60° in 10 seconds. What is the time taken (in seconds) by the boat to reach the lighthouse from its initial position?

A boat is sailing towards a lighthouse of height 20√3 m at a certain speed. The angle of elevation of the top of the lighthouse changes from 30° to 60° in 10 seconds. What is the time taken (in seconds) by the boat to reach the lighthouse from its initial position? Correct Answer 15

Let the point where the angle of elevation of the boat is 60°be A

And the point where the angle of elevation of the boat is 30°be B

Also, let the top of lighthouse be O and bottom be C

Given: height of lighthouse = 20√3 m

In ∆AOC

⇒ tan60° = 20√3/BC

⇒ √3 = 20√3/BC

⇒ BC = 20 m

In ∆AOC

⇒ tan30° = 20√3/AC

⇒ 1/√3 = 20√3/AC

⇒ AC = 60 m

Now, time taken to cover AB = 10 sec

So, speed of boat = (60 - 20)/10 = 4m/s

∴ Time taken by the boat to go from A to C = 60/4 = 15 seconds

Related Questions

A boat is sailing towards a lighthouse of height 20√3 m at a certain speed. The angle of elevation of the top of the lighthouse changes from 30° to 60° in10 seconds. What is the time taken (in seconds) by the boat to reach the lighthouse from its initial position?
What is the distance covered by boat N upstream in 5 hours? Which of the following option is sufficient alone to find the answer? A) Boat M is travelling downstream with 20% more downstream speed of boat N. Speed of boat M in still water is 10% more than the speed of boat N in still water. B) Boat M and Boat N are travelling downstream with speed 33 km/hr and 40 km/hr respectively and speed of boat M is still water is 2 times the speed of stream. C) Speed of boat M in still water is 6 km/hr less then speed of boat N in still water and speed of stream is 10 km/hr. D) Speed of stream is ½ times the speed of boat N in still water and downstream speed of boat M is 44 km/hr. E) Speed of stream is 10 km/hr and ratio of upstream speed of boat M and boat N is 3 : 2 respectively.
In the following question, two statements are numbered as A and B. On solving these statements we get quantities A and B respectively. Solve for the both quantities and chose the correct option. Quantity A: The ratio of speed of boat to speed of stream is 2 : 1, If the boat travels 162 km and come back to starting point in 36 hour. What is the difference between the time taken by the boat to go upstream and the time taken by the boat to go downstream? Quantity B: The speed of the stream is 6 km/hr and the distance travelled by the boat is 60 km. If the boat covered half distance upstream with usual speed and other half with double its speed, then it takes 7.5 hours less time than usual time to go upstream. Find the total time taken by the boat to go upstream and downstream?
The angle of elevation of the top of a 36 m tall tower from the initial position of a person on the ground was 60 deg. She walked away in a manner that the foot of the tower, her initial position and the final position were all in the same straight line. The angle of elevation of the top of the tower from her final position was 30 deg. How much did she walk from her initial position?
Questions below followed by two quantities. Find the relation between them. The table shows the distance travelled by five different boats upstream, the speed of the boat in still water and the time taken by them to cover the upstream distance. Boats Upstream distance Speed of boat Time taken  A  240 km  15 km/hr  20 hr  B  150 km  10 km/hr  25 hr  C  350 km  20 km/hr  50 hr  D  96 km  8 km/hr  16 hr  E  126 km  26 km/hr  9 hr   Quantity I: Boat B travel 238 km distance downstream in certain time. How much downstream distance boat D will cover at the same time? Quantity II: Boat E travel 722 km distance downstream in certain time. How much downstream distance boat A will cover at the same time?
Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30º and 45º respectively. If the lighthouse is 100 m high, the distance between the two ships is:
Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30° and 45° respectively. If the lighthouse is 100 m high, the distance between the two ships is:
Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30º and 45º respectively. If the lighthouse is 200 m high, the distance between the two ships is:
The speed of Boat P is 3 km/h more than the speed of Boat Q. The time taken by Boat Q to travel a distance of 30 km downstream is 30 minutes more than the time taken by Boat P to travel the same distance downstream. If the speed of the current is 1/3 of the speed of Boat Q, then what is the speed of Boat P?
A map shows the elevations of Darjeeling, Gangtok, Kalimpong, Pelling, and Siliguri. Kalimpong is at a lower elevation than Gangtok, Pelling is at a lower elevation than Gangtok. Pelling is at a higher elevation than Siliguri. Darjeeling is at a higher elevation than Gangtok. Which of the following statements can be inferred from the paragraph above? i. Pelling is at a higher elevation than Kalimpong ii. Kalimpong is at a lower elevation than Darjeeling iii. Kalimpong is at a higher elevation than Siliguri iv. Siliguri is at a lower elevation than Gangtok