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A moving boat is observed from the top of a $150 m$ high cliff moving away from the cliff. The angle of depression of the boat changes from $60 °$ to $45 °$ in 2 minutes, then the speed of the boat in m/ min is:

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313m/min

311m/min

317m/min

315m/min

answer is A.

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Detailed Solution

Given,
Height of the cliff = 150m
The angle of depression of the boat changes from

60 °

45 °

in 2 minutes.
Consider the figure,
Question Image

The distance covered by boat,

y = 150 tan 45 ° − 150 tan 60 ° ⇒ y = 150 − 1503 ⇒ y = (150 − 503) m

We know,

Speed = \frac{Distance}{Time}

The speed of boat,

s p e e d = 150 − 503 2 ⇒ s p e e d = 75 − 253 ⇒ s p e e d = 317 m / min

The speed of boat is 317 m/min
Therefore, option 1 is correct.

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