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From a 15 m high bridge on the river, the angle of depression of a boat is 30°. If the speed of the boat be 6 Km/h, then the time taken by the boat to reach exactly below the bridge will be :
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- 9 √3 second
- 19 / √3 second
- 3 √3 second
- None of these
Correct Option: A
Let us draw the figure from the given question.
Let, C be the initial position of the boat, and A be the point on the top of the bridge from where the angle of depression of the boat is 30°. Distance ( AB ) = 15 m,
| In triangle ACB , tan30° = | AB |
| BC |
| ⇒ | BC = | = | = | 15 √3m. | ||
| tan30° | 1 / √3 |
| Speed of the boat = | 6 Km/h = 6 x | 5 | m/s = | 5 | m/s |
| 18 | 3 |
| ∴ | Time required = | Distance | = | 15 √3 | = | 9 √3 second . |
| Speed | 5 / 3 |
