Question
Download Solution PDFA 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
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCalculation:
CD = 10 unit
In Δ ABC
tan 45 = AB/BC
BC = AB --- (1)
In ΔABD
tan 60 = AB/BD
⇒ √3 = AB/BD
⇒ AB = √3 BD
BC = √3 BD [From equation (1)]
BC = BD + CD
⇒ √3 BD – BD = CD
⇒ BD (√3 – 1) = 10
⇒ BD = 10/(√3 – 1) × [(√3 + 1)/(√3 + 1)]
⇒ BD = 10 (√3 + 1)/2
⇒ BD = 5 (1.732 + 1)
⇒ BD = 5 × 2.732
⇒ BD = 13.66 unit
⇒ 10 unit = 10 min
⇒ 13.66 unit = 13 min 40 sec
Short Trick:
(√3 – 1) unit = 10 min
1 unit = 10/(√3 - 1) × [(√3 + 1)/(√3 + 1)]
⇒ 1 unit = 10 (√3 + 1)/2 = 5 (1.732 + 1) = 5 × 2.732 = 13.66
⇒ 13.66 = 13 min 40 sec
Last updated on Jun 13, 2025
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