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drashanhparekh123
21.05.2020 •
Mathematics
A hot air balloon rising vertically is tracked by an observer located 4 km from the lift‑off point. At a certain moment, the angle between the observer's line of sight and the horizontal is π/5, and it is changing at a rate of 0.4 rad/min. How fast is the balloon rising at this moment? Let y be the height of the balloon (in km), t be time (in minutes), and θ the angle between the line‑of‑sight and the horizontal (in radians).
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Ответ:
1.22 km/min
Step-by-step explanation:
Let Q be baloon height at a time t. Our goal is to determine the speed of the baloon at the moment.
The dy / dt velocity of the baloon when = π/5?
So we can restate the question as follows:
Owing to the fact d / dt = 0.2 rad / min at some stage = π/5
from fig:
tanθ = y/4
Differentiating w.r.t "t"
sec2 θ * dθ/dt = 1/4(dy/dt)
=> dy/dt = (4/cos2 θ)dθ/dt
At the given moment θ = and dθ/dt = 0.2 rad/min.
dy/dt = (4/cos2)* (0.2)
= 1.22 km/min
And the velocity of the baloon currently is 1.22 km / min.
Ответ:
And as perimeter is just the sum of length of all side, we will calculate the length of each side and then sum them up.
1. Side AB:
d₁= √34
2.Side AC
d₂=2√10
3.Side BC
d₃=√58
Perimeter
P=19.77