Question
A boat is being rowed away from a cliff 240 m high. From the top of the cliff, the angle of depression of the boat changes from 60° to 45° in 3 minutes. What is the speed of the boat?
According to the figure above: tan 45° = 240/(a + b) ⇒ 1 = 240/(a + b) ⇒ a + b = 240 Also, tan 60° = 240/a ⇒ √ 3 = 240/a ⇒ a = 240/ √ 3 ⇒ a = 80√ 3 = 138.5 ∴ b = 240 - 138.5 = 101.5 ⇒ The boat covers a distance of 101.5 m in 3 minutes. ∴ Speed of the boat = (101.5 x 60)/(3 x 1000) km/h = 2.03 km/hMore Height and Distance Questions
- 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...
- There is a fire in the building. A man on the top of the building see a Fire brigade van coming towards it. If it takes 8 minutes for the angle of depressi...
- A vertical tower stands on a horizontal plane and is surmounted by a vertical flag staff of height h. At a point on the plane, the angle of elevation of th...
- 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...
- The length of the shadow of a vertical tower increases by 9 m on horizontal ground when the height of the sun changes from 45° to 30 ° , then find ...
- The distance between two parallel poles is 65√3 m. The angle of depression of the top of the second pole when seen from the top of first pole is 30o....
- The shadow of a pole 24m long is 56m. Then what will be the approximate shadow of building 40m high at the similar situation?
- A pole 21 m high casts a shadow 7√3 m long on the ground. Find the angle of elevation
- 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. Wh...
- A man 1.5 m tall is 22.5 m away from a tower 24 m high. Determine the angle of elevation of the top of the tower from the eye of the observer.
Relevant for Exams:
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
