The difference in the distance of the balloon at the two locations at
which the angle of elevation is measured is the distance travelled.
Response:
- The distance traveled by the balloon during the interval is approximately 100.46 m
How is the distance traveled by the balloon estimated?
Height of the girl = 1.2 m
Height of the balloon above the ground = 88.2 m
Angle of elevation of the balloon = 60°
Angle of elevation after the balloon after an interval of time = 30°
Required:
Distance traveled by the balloon.
Solution:
Height of the balloon over the girl = 88.2 m - 1.2 m = 87 m
Initial horizontal distance of the balloon from the girl, d₁, is given as
follows;
[tex]d_1 = \dfrac{87}{tan(60^{\circ})} \approx \mathbf{ 50.23}[/tex]
Initial horizontal distance of the balloon from the girl, d₁ ≈ 50.23 m
Horizontal distance after the time interval, d₂, is given as follows;
[tex]d_2 = \dfrac{87 \, m}{tan(30^{\circ})} \approx \mathbf{150.69 \, m}[/tex]
The distance travelled by the balloon during the interval, d = d₂ - d₁, which gives;
d ≈ 150.69 m - 50.23 m = 100.46 m
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