Answer:
a) the first vector has magnitude 58 cm and the angle is 15 measured clockwise from the positive side of the x-axis
b) the second vector, the magnitude is 55.7 cm and the angle is 35 half from the negative side of the x-axis in a clockwise direction
c) the magnitude is 54.2 cm with an angle of 18 measured counterclockwise from the x-axis
Explanation:
For this exercise we draw a Cartesian coordinate system in this system: East coincides with the positive part of the x-axis and North with the positive part of the y-axis.
a) the first vector has magnitude 58 cm and the angle is 15 measured clockwise from the positive side of the x-axis
b) the second vector, the magnitude is 55.7 cm and the angle is 35 half from the negative side of the x-axis in a clockwise direction
c) the magnitude is 54.2 cm with an angle of 18 measured counterclockwise from the x-axis
In the attachment we can see the representation of the three vectors
Answer:
The height of the water above the hole in the tank is 58 mm
Explanation:
In order to solve this problem we need to draw a sketch of the dimensions that include the input variables of the problem.
Where:
x = 0.579[m]
y = 1.45 [m]
Using the following kinematic equation we can find the time that takes the water to hit the ground, and then with this time, we can find the velocity of the water in the x-component.
It is necessary to clarify the value of each of the respective variables below
y = - 1.45 [m] "It is negative because this point is below the water outlet"
yo = 0
vo = 0 "The velocity is zero because the component of the speed on the Y-axis does not exist"
therefore:
![-1.45=0.5*(-9.81)*t^{2} \\t = \sqrt{\frac{1.45}{0.5*9.81} } \\t = 0.543[s]](https://tex.z-dn.net/?f=-1.45%3D0.5%2A%28-9.81%29%2At%5E%7B2%7D%20%5C%5Ct%20%3D%20%5Csqrt%7B%5Cfrac%7B1.45%7D%7B0.5%2A9.81%7D%20%7D%20%5C%5Ct%20%3D%200.543%5Bs%5D)
The next step is to determine the velocity in component x, knowing the time.
![v=\frac{x}{t} \\v=\frac{0.579}{.543} \\v = 1.06[m/s]](https://tex.z-dn.net/?f=v%3D%5Cfrac%7Bx%7D%7Bt%7D%20%5C%5Cv%3D%5Cfrac%7B0.579%7D%7B.543%7D%20%5C%5Cv%20%3D%201.06%5Bm%2Fs%5D)
Now using torricelli's law we can find the elevation.
![v=\sqrt{2*g*h} \\h=\frac{v^{2} }{2*g} \\h=\frac{1.06^{2} }{2*9.81} \\h= 0.057[m] = 57.95[mm]](https://tex.z-dn.net/?f=v%3D%5Csqrt%7B2%2Ag%2Ah%7D%20%5C%5Ch%3D%5Cfrac%7Bv%5E%7B2%7D%20%7D%7B2%2Ag%7D%20%5C%5Ch%3D%5Cfrac%7B1.06%5E%7B2%7D%20%7D%7B2%2A9.81%7D%20%5C%5Ch%3D%200.057%5Bm%5D%20%3D%2057.95%5Bmm%5D)
It was important because it tells why the denser material had sunken and the lighter is floating on the surface.
<u>Explanation:</u>
Eventually, after around 500 million years, our young planet's temperature warmed to the liquefying purpose of iron—about 1,538° Celsius (2,800° Fahrenheit). This crucial crossroads in Earth's history is known as the iron fiasco. The iron fiasco permitted more prominent, progressively quick development of Earth's liquid, rough material.
We also know that at one point all the material in the planet was molten because the denser material had sunk and the lighter was floating.
Planet Y has rotated by 135.5° through during this time.
To find the answer, we need to know about the relation between angle and radius of orbit.
<h3>What's the expression of angle in terms of radius?</h3>
- Angle= arc/radius
- As arc = orbital velocity × time,
angle= (orbital velocity × time)/radius
- Orbital velocity= √(GM/radius), G= gravitational constant and M = mass of sun
- So, angle = (√(GM)× time)/radius^3/2
<h3>What's is the angle rotated by planet Y after 5 years, if ratio of the radius of orbit of planet X and Y is 4:3 and planet X is rotated by 88°?</h3>
- Let Ф₁= angle rotated by planet Y, Ф₂= angle rotated by planet X
- As time = 5 years ( a constant)
- Ф₁/Ф₂= (radius of planet X / radius of planet Y)^(3/2)
- Ф₁= (radius of planet X / radius of planet Y)^(3/2) × Ф₂
= (4/3)^(3/2) × 88°
= 135.5°
Thus, we can conclude that Planet Y has rotated by 135.5° through during this time.
Learn more about the orbital velocity here:
brainly.com/question/22247460
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Answer:
right one is more efficient
Explanation:
