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Sagot :
The Pythagoras' theorem and the uniform motion allows to find the answer for the rate of change of distance is
v = 32.3 m / s
The distance is the length of the segment that a white house wing with the helicopter, this can be found using the Pythagoras' theorem
R = [tex]\sqrt{x^2 + y^2}[/tex]
Where R is the distance, x is the horizontal distance where the helicopter flies and y is the vertical distance that corresponds to the flight height
y = 500 m
Since the helicopter flies at constant speed, we can use the uniform motion relation
[tex]v_h[/tex] = [tex]\frac{x}{t}[/tex]
x = [tex]v_h[/tex]t
Where [tex]v_h[/tex] is the speed of the helicopter and t is the time
We substitute
r = [tex]\sqrt {(V_h \ t)^2 + y^2}[/tex]
Kinematics defines velocity as the change of position in the unit of time
[tex]v = \frac{dR}{dt}[/tex]
[tex]v = \frac{1}{2} \ \frac{2 ( v_h t) v_h}{ \sqrt{(v_h t)^2 + y^2} }[/tex]
[tex]v = \frac{v_h^2 \ t}{ \sqrt{(v_h t)^2 + y^2} }[/tex]
This expression is the change in distance as a function of time for a given speed. In the exercise, this speed is requested for a time of one minute, for the helicopter speed of
v = 2km/min ([tex]\frac{1000m}{1km}[/tex] ) ( [tex]\frac{1 min}{60s}[/tex]) = 33.33 m / s
Let's calculate
v = [tex]\frac{33.33^2 \ 60 }{ \sqrt{ )33.3 \ 60)^2 +500^2} }[/tex]
v = 32.3 m / s
In conclusion using the Pythagoras' theorem and the uniform motion we can find the answer for the rate of change in distance is
v = 32.3 m / s
Learn more here: brainly.com/question/343682
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