A man in a boat rowing away from a lighthouse 100m high takes 2 minutes to change the angle of elevation of the top of light house from 60° to 30`. Find the speed of the boat in metres per minute. [ Use √3 = 1.732]
Answers
Answer:
Speed of the Rower = 57.785 meters / min
Step-by-step explanation:
Please see the attached figure for reference.
Height of tower H = 100 m
At the start of the rowing, Distance of the boat from the tower = x
Boat travels distance in 2 mins = y
Initial angle of elevation = 60°
Final angle of elevation after 2 mins = 30°
Let initial triangle formed by the Boat position be - ΔABC
where ∠B = 60°
Final triangle formed by the rower position be - ΔADC
where ∠D = 30°
Applying trignometric rules to ΔABC,
Tan (B) = Opposite length / Adjecent length
Tan (60°) = 100 / x
x = 100 / 1.732
x = 57.74 m .... (1)
Applying trignometric rules to ΔADC,
Tan (D) = Opposite length / Adjecent length
Tan (30°) = 100 / (x+y)
0.577 = 100 / (x+y)
x+y = 173.31 m .... (2)
Substituting value x from eq.1
57.74 + y = 173.31
y = 173.31 - 57.74
∴ y = 115.57 m ... (3)
Speed of the Boat = Distance traveld / time taken
Speed of the Boat = y / 2min
Speed of the Boat = 115.57 / 2 m/min
Speed of the Boat = 57.587 meters / min
