The angle of elevation from Jet fighter. A ground on 60 degree after a flight takeoff 15 seconds the angle of elevation 30 degree if you at speed of 720 km per hour then find the constant height reached at the flying
I will assume the following:
when t = 0 , angle of elevation is 60°
when t = 15 seconds, angle of elevation is 30°
horizontal speed is 720 km/h
let the constant height that the plane is flying be h m
I have a right-angled triangle with height h m, base of x m
and base angle of Ø° degrees
speed of 720 km/h = 720000/3600 m/s = 200 m/s
tanØ = h/x -------> h = x tanØ
case 1: when Ø = 60° , tan 60° = √3 , height = h, base = x
h = x√3
case 2: when Ø = 30° , horizontal distance = x + 15(200) = x + 3000
tan30° = 1/√3
h = (x + 3000)(1/√3) = (x+3000)/√3
√(x+3000)/√3 = x√3
x+3000 = 3x
x = 1500
then in : h = x√3
h = 1500√3 or appr 2598 m or 2.598 km
typo in 5th last line:
should be
(x+3000)/√3 = x√3 , not √(x+3000)/√3 = x√3
has no effect on what follows
750 km/hr = 200 m/s
so, in 15 seconds, the plane has gone 3000m
Draw a diagram. It should be clear that if the plane's height is h, then
h cot30° - h cot60° = 3000
h = 3000/(√3 - 1/√3) = 1500√3 meters
To find the constant height reached by the flying jet fighter, we can use the concepts of trigonometry and basic physics. Here are the step-by-step calculations:
1. Convert the speed from kilometers per hour to meters per second:
Speed in meters per second = Speed in kilometers per hour * (1000 meters / 1 kilometer) * (1 hour / 3600 seconds)
Speed in meters per second = 720 km/hr * (1000/1) * (1/3600)
Speed in meters per second = 200 meters/second (approximately)
2. Determine the time it took for the jet fighter to reach a constant height by subtracting the time for the angle of elevation to change from 60 degrees to 30 degrees:
Time for angle change = 15 seconds
3. Let's assume the constant height reached by the jet fighter is represented by 'h' (in meters).
4. In the time it took for the angle of elevation to change, the horizontal distance traveled by the jet fighter is given by:
Horizontal distance = Speed * Time
Horizontal distance = 200 m/s * 15 s
Horizontal distance = 3000 meters
5. To find the height 'h', we will use the tangent of the angle of elevation:
tan(30 degrees) = h / Horizontal distance
tan(30 degrees) = h / 3000
6. Rearrange the equation to solve for 'h':
h = tan(30 degrees) * 3000
7. Calculate the value of 'h':
h ≈ 3000 * 0.577 (using tan(30 degrees) ≈ 0.577)
h ≈ 1731 meters
Therefore, the constant height reached by the flying jet fighter is approximately 1731 meters.