A person from the top of a hill observes a vehicle moving towards him at a uniform speed. It takes 10 minutes for the angle of depression to change from 45? to 60?. After this the time required by the vehicle to reach the bottom of the hill is
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 13 min 40 sec
| Application |
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AB = height of hill = h metre Let the speed of the vehicle be v meter/minute. Time is taken to reach B from D = t minutes CD = 10v metre BD = vt metre In triangle ABC, Tan 45 = AB/BC 1 = h/BC metre BC = h = (10v + vt) metre ....(i) In triangle ABD, Tan 60 = AB/BD √3h/vt h = √3vt 10v + vt = √3 vt 10 = √3 t - t 10 = t (√3 - 1) t = 10/ (√3 - 1) 10(√3 + 1)/(√3 - 1)(√3 + 1) = 10(√3 + 1)/2 5 (1.732 + 1) = 5 × 2.732 13.66 minutes 13 minutes 40 seconds |