SSC CGL 16 Aug 2017 Shift 1 Paper

Question : 69 of 100

Marks: +1, -0

A boat is sailing towards a lighthouse of height

20√3

m at a certain speed. The angle of elevation of the top of the lighthouse changes from 30° to 60° in 10 seconds. What is the time taken (in seconds) by the boat to reach the lighthouse from its initial position?

Validate

Solution:

According to the question,

{\In} \Δ A D C,

\tan 60°= {20 √{3}}/{D C}

⇒

√3= {20 √{3}}/{D C}

∴

DC = 20 \m

Again, in ΔABC,

\tan 30°= {20 √{3}}/{B D+D C}

⇒

1/√3= {20 √{3}}/{B D+D C}

⇒

{B D+D C}=60

∴

BD= 40 \m

Speed of boat

= {40}/{10}=4 {\m} \/ {\s}

Hence, required time

= {B D+D C}/{4}= {40+20}/{4}

= {60}/{4}=15 {\sec}

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