Discussion
A boat is being rowed away from a cliff 150m high. At the top of the cliff the angle of depression of the boat changes from 60º to 45º in 2 minutes. Find the speed of the boat.
Answer: A
The cliff is 150 m, and the angle of depression falls as the boat moves away.
\[ d_{60} = \frac{150}{\tan 60^{\circ}} = \frac{150}{\sqrt{3}} = 50\sqrt{3} = 86.6 \text{ m} \]
\[ d_{45} = \frac{150}{\tan 45^{\circ}} = 150 \text{ m} \]
\[ \text{distance rowed} = 150 - 86.6 = 63.4 \text{ m in } 2 \text{ minutes} \]
\[ \text{speed} = \frac{63.4}{2} = 31.7 \text{ m/min} = 31.7 \times \frac{60}{1000} = 1.90 \text{ km/h} \]
Converting metres per minute to km/h means multiplying by 60 and dividing by 1000 - the same as multiplying by 0.06.
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