Question
A boat is being rowed away from a cliff 270 m high. From the top of the cliff, the angle of depression of the boat changes from 60° to 45° in 2 minutes. What is the speed of the boat?
According to the figure above: tan 45° = 270/(a + b) ⇒ 1 = 270/(a + b) ⇒ a + b = 270 Also, tan 60° = 270/a ⇒ √ 3 = 270/a ⇒ a = 270/ √ 3 ⇒ a = 90√ 3 = 155.8 ∴ b = 270 - 155.8 = 114.2 ⇒ The boat covers a distance of 114.2 m in 2 minutes. ∴ Speed of the boat = (114.2 x 60)/(2 x 1000) km/h = 3.4 km/hMore Height and Distance Questions
- The angle of elevation of an aeroplane from a point on the ground is 60°. After 15 seconds flight the elevation changes to 30°, if the aeroplane is flying ...
- A pole 6 m high casts a shadow 2√3 m long on the ground. Find the angle of elevation
- A Navy captain going away from a lighthouse at the speed of 4[(√3) – 1] m/s. He observes that it takes him 1 minute to change the angle of elev...
- A tree breaks due to a storm and the top touches the ground 30 meters away from its base, making a 30-degree angle with the ground. What was the height of ...
- There are two houses of the same height on both sides of a 40-meter wide road. From a point on the road, elevation angles of the houses are 30° and 60° res...
- A tree of height 'h' meters is partially bent at a certain point above the ground, causing its top to touch the ground at a distance of 12 meters from its ...
- A man whose height is 1.5 metres is standing 24√3 metres away from a light pole. The angle of elevation from his head to the top of the light pole is...
- Two men are on opposite sides of a tower of 75 m height. If they measure the elevation of the top of the tower as 30deg; and 45deg; respectively then the d...
- From a point on level ground, the angle of elevation of the top of a vertical tower is 30°. On moving 30 m closer to the tower, the angle of elevation beco...
- A man 3 m tall is 19 m away from a tower 22 m high. Determine the angle of elevation of the top of the tower from the eye of the observer.
Hey! Ask a query
Please enter email id
The email must be a valid email address.
Please enter Mobile Number
Please enter valid Mobile Number
Please enter your Doubt
