Question

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

Answer 1

Answer:

★ 31.7 m/min or 1902 m/hr ★

Step-by-step explanation:

Given:

• Boat is observed from the top of a 150 m high cliff
• Angle of depression changes from 60° to 45°
• Time taken 2 minutes

To Find:

• Speed of boat in m/Mon

Solution:

★ Let AB height of Cliff = 150 m ★

→BC = x and DC = 2 minutes ←

† Let the speed be S

In ∆ ABC

$\small\implies{\sf }$ tan60° = perpendicular/base

$\small\implies{\sf }$ tan60° = AB/AC

$\small\implies{\sf }$ √3 = 150/x ( tan60° = √3 )

$\small\implies{\sf }$ x√3 = 150 ( By Cross multiplication )

$\small\implies{\sf }$ x = 50√3m

Time given is 2 minutes

★ Now, In ∆ABD ★

$\small\implies{\sf }$ tan45° = perpendicular/base

$\small\implies{\sf }$ tan45° = AB/BD

$\small\implies{\sf }$ 1 = 150/2S + x

$\small\implies{\sf }$ 2S + x = 150 ( By Cross multiplication )

$\small\implies{\sf }$ 2S + 50√3 = 150 ( Putting value of x )

$\small\implies{\sf }$ 2S = 150 – 50√3

$\small\implies{\sf }$ 2S = 50 ( 3 – √3 )

$\small\implies{\sf }$ 2S = 50( 1.268 )

$\small\implies{\sf }$ 2S = 63.4

$\small\implies{\sf }$ S = 63.4/2 = 31.7 m/min

Hence, Speed of boat in m/min is 31.7

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★ Also check the attached picture ★