Question

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 degree into minutes find the speed of the boat

Answer 1

Step-by-step explanation:

Given: AB = Height of cliff = 150 m

Let BC =x m

Let CD = y m

Then on ΔABC,

tan 60° = AB/BC

⇒ √3 = 150/x

⇒ x = 150√3 ………... (1)

In ΔABD,

tan 45° = AB/BD

⇒ 1 = 150/(x+y)

⇒ x+y = 150 ………………(2)

From equation (1) and (2), we get:

y = 150 –x = 150 – (150/√3)

= 150 – (150√3/3) (multiplying and dividing the later term by √3)

= (150 – 50√3)

Now, time taken by the boat to move from point C to point D = 2 min = 2/60 hr = 1/30 hr

Distance = Speed × Time

∴ Speed = Distance/Time

= (150 – 50√3)/(1/30)

= 30 × (150 – 50√3)

= (4500 – 1500√3) m/hr

= 1500(3 - √3) km/hr

= 1901.92 kmm/hr

= 1.90192 km/hr

Answer 2

Answer:

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Step-by-step explanation:

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