A balloon moving upward and observe at 10:00 Hrs at a distance from point of ballon to 300 mtres with a angle of elevation 30degree after 10:02 the angle of elev. ecomes 60 degree find the speed of balloon?
Answers
Answer:
150 m/s
Step-by-step explanation:
A balloon moving upward and observe at 10:00 Hrs at a distance from point of ballon to 300 mtres with a angle of elevation 30degree after 10:02 the angle of elev. becomes 60 degree find the speed of balloon?
At 10:00 Hrs
Hypotenuse = 300 m ( distance of balloon)
Angle of Elevation = 30°
Sin θ = Perpendicular / Hypotenuse
=> Sin 30° = ( Vertical height of Baloon) / 300 m
=> 1/2 = height of Baloon /300
=> height of Baloon = 150 m
Cos θ = Base / Hypotenuse
=> Cos 30° = ( Horizontal distance of Baloon) / 300 m
=>√3/2 = Horizontal distance of Baloon /300
=> Horizontal distance of Baloon = 150√3 m
At 10:02 Hrs
Angle of Elevation = 60°
Horizontal distance of Baloon = 150√3 m ( as Moving vertically upward)
Tan θ = Perpendicular / Base
=> Tan 60° = (height of Ballon )/ Horizontal distance of Baloon
=> √3 = height of Ballon / 150√3
=> height of Ballon = 450 m
Vertical distance moved by Baloon = 450 - 150 = 300 m
Time = 2 Mins
Speed = 300/2 = 150 m/s
the speed of balloon = 150 m/s