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. What is the speed of theboat in m/h?

Height of cliff = 150 m

Step 1: Use formula
tan θ = height / distance

Step 2: Initial position (60°)
tan 60 = 150 / d1
√3 = 150 / d1
d1 = 150 / √3 = 50√3 ≈ 86.6 m

Step 3: Final position (45°)
tan 45 = 150 / d2
1 = 150 / d2
d2 = 150 m

Step 4: Distance travelled
Distance = d2 - d1
= 150 - 86.6
= 63.4 m

Step 5: Time conversion
2 minutes = 2/60 hours = 1/30 hour

Step 6: Speed
Speed = distance / time
= 63.4 ÷ (1/30)
= 63.4 × 30
= 1902 m/h

Final Answer: Speed ≈ 1900 m/h