A plane decides to travel along AB towards the North with a velocity of V.
1 answer:
Step-by-step explanation:
The wind has a speed of w and a direction α with the vertical. The x component of that speed is w sin α. The y component is -w cos α.
In order to stay on the north trajectory AB, the plane must have a horizontal speed of -w sin α. The plane's speed is v, so using Pythagorean theorem, the y component of the plane's speed is:
v² = (-w sin α)² + vᵧ²
v² = w² sin²α + vᵧ²
vᵧ = √(v² − w² sin²α)
The total vertical speed is therefore √(v² − w² sin²α) − w cos α.
If a is the length of AB, then the time is:
t = a / [√(v² − w² sin²α) − w cos α]
To rationalize the denominator, we multiply by the conjugate.
t = a / [√(v² − w² sin²α) − w cos α] × [√(v² − w² sin²α) + w cos α] / [√(v² − w² sin²α) + w cos α]
t = a [√(v² − w² sin²α) + w cos α] / (v² − w² sin²α − w² cos²α)
t = a [√(v² − w² sin²α) + w cos α] / (v² − w²)
You might be interested in
Answer:
In 2010 the population become 206,123,000.
Step-by-step explanation:
Consider the provided equation.
Where P represents the population in millions.
We need to determine the year in which the country had population of 206,123,000.
As P is in millions so divide 206,123,000 by one million.
Substitute P = 206.123 in above equation.
30 year from 1980 the population become 206,123,000.
In 2010 the population become 206,123,000.