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Sudhanshu Singh

· started a discussion

· 1 Months ago

i (Question:134191.0)

total time 20+10=30

Question:
A man on the top of a rock rising on a sea-shore obeserves a boat coming towards it. If it takes 20 minute for the angle of depression to change from 30° to 60°, In how much more time will the boat reach the shore?
Options:
A) 20 minute
B) 30 minute
C) 10 minute 
D) 15 minute
Solution:


From figure, tan 60° = \(\cfrac{h}{y}\)

⇒ h= y√3 …(i)

and tan30° = \(\cfrac{h}{x+y}\)

⇒ \(\cfrac{1}{√3 }\) = \(\cfrac{y√3 }{x+y}\) [using (i)]

∴ 3y=x+y

⇒ 2y = x ⇒ y = \(\cfrac{x}{2}\)

∵ Time taken to cover a distance from A to B = 20 minute

∴ time taken to cover a unit distance = \(\cfrac{20}{x}\) minute

∴ For distance ‘y’ time taken = \(\cfrac{20}{x}\) × y

= \(\cfrac{20}{x}\) × \(\cfrac{x}{2}\) = 10 minute

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