1.  A ship is approaching an observation tower. If the time taken by the ship to change the angle of elevation from 30° to 45° is 10 minutes, then find the time the ship will take to cover the remaining distance and reach the observation tower assuming the ship to be travelling at a uniform speed.
A. 15 minutes 20 seconds
B. 13 minutes 40 seconds
C. 16 minutes 40 seconds
D. Cannot be determined

Answer: Option

Explanation:


Let AB be the observation tower and h be its height.

Also, let the ship be at C when the angle of elevation is 30° and at D when the angle of elevation is 45°.

The time taken by the ship to travel from C to D is 10 minutes and we need to find out the time the ship will take to reach B from D.

 tan 30º = AB/CB = h / CB = 1/ 3

 CB = 3 x h

tan 45º = AB / DB = h / DB = 1

 DB = h

 CD = CB – DB = (3h – h) = h(3– 1)

Now, as h(3 – 1) distance is covered in 10 minutes, a distance of h is covered in = 13.66 minutes = 13 minutes 40 seconds