A 1130-kg car is held in place by a light cable on a smooth (frictionless) ramp. The cable makes an angle of 31.0° above the sur
1 answer:
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Answer:
d= 64.1 km θ = 36.4º
Explanation:
a) In order to find the plane's straight-line distance from the starting point, we need to know the coordinates of the final and initial position of the plane, so we can find the total displacement, as the difference between the final and initial position.
If we choose to put our origin at the initial point of trajectory, we have that (x₀, y₀) = (0, 0)
In order to find the position of the plane after finishing the flight, we need to find its final coordinates (x₁, y₁).
In order to get x₁, we need to add the x-coordinate after flying 45º north of east, and the Δx after completing the flight in a direction 25º of east, that we can find applying trigonometry, as follows:
x₁ = 37.0 km * cos 45º + 28.0 km* cos 25º = 51.6 Km
Appying the same considerations for the y-coordinate, we have:
y₁ = 37.0 km * sin 45º + 28.0 km* sin 25º = 38.0 km
Now, as the initial position coincides with the origin, the distance in a straight line from this point to the origin, is just the hypotenuse of the triangle determined by the coordinates (x₁, y₁) and (0,0), as follows:
The geographic direction of the displacement vector (which coincides in magnitude with the distance we have just found), is just the angle that this distance forms with the east axis, that we can find getting the tangent of this angle as follows:
tg θ =
⇒ θ = 36.4º North of East (counterclockwise from the east axis).
Complete Question
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Answer:
The total pressure is
The temperature at the bottom is
Explanation:
From the question we are told that
The length of the glass tube is
The length of water rise at the bottom of the lake
The depth of the lake is
The air temperature is
The atmospheric pressure is
The density of water is
The total pressure at the bottom of the lake is mathematically represented as
substituting values
According to ideal gas law
At the surface the glass tube not covered by water at surface
Where is the volume of
At the bottom of the lake
Where is the volume of the glass tube not covered by water at bottom
and i the temperature at the bottom
So the ratio between the temperature at the surface to the temperature at the bottom is mathematically represented as
substituting values
=>
