-
A boat is moving away from an observation tower. It makes an angle of depression of 60° with an observer’s eye when at a distance of 50 metre from the tower. After 8 seconds, the angle of depression becomes 30°. By assuming that it is running in still water, the approximate speed of the boat is :
-
- 33 km/hr
- 42 km/hr
- 45 km/hr
- 50 km/hr
Correct Option: C
AB = Height of observation tower = h metre
C and D = Positions of boat
BC = 50 metre
Let, CD = x metre
∠ACB = 60° = ∠EAC
∠ADB = 30° = ∠EAD
In ∆ABC,
| tan 60° = | |
| BC |
| ⇒ √3 = | |
| 50 |
⇒ h = 50√3 metre
In ∆ABD,
| tan 30° = | |
| BD |
| ⇒ | = | ||
| √3 | 50 + x |
⇒ 50 + x = 50√3 × √3 = 150
⇒ x = 150 – 50 = 100 metre
| ∴ Speed of boat = | |
| Time |
| = |  |  | m/sec. | |
| 8 |
| = | | × | | kmph | ||
| 8 | 5 |
