Answer:
Explanation:
To solve this problem we use the Momentum's conservation Law, before and after the girl catch the ball:
(1)
At the beginning the girl is stationary:
(2)
If the girl catch the ball, both have the same speed:
(3)
We replace (2) and (3) in (1):
We can now solve the equation for v_{f}:
The hoop is attached.
Consider that the friction force is given by:
F = μ·N
= μ·m·g·cosθ
We also know, considering the forces of the whole system, that:
F = -m·a + m·g·sinθ
and
a = (1/2)·<span>g·sinθ
Therefore:
</span>-(1/2)·m·g·sinθ + m·g·sinθ = <span>μ·m·g·cosθ
</span>(1/2)·m·g·sinθ = <span>μ·m·g·cosθ
</span>μ = (1/2)·m·g·sinθ / <span>m·g·cosθ
= </span>(1/2)·tanθ
Now, solve for θ:
θ = tan⁻¹(2·μ)
= tan⁻¹(2·0.9)
= 61°
Therefore, the maximum angle <span>you could ride down without worrying about skidding is
61°.</span>
<h3><u>Answer</u>;</h3>
= 22°
<h3><u>Explanation</u>;</h3>
- According to Snell's law, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant. The constant value is called the refractive index of the second medium with respect to the first.
- Therefore; Sin i/Sin r = η
In this case; Angle of incidence = 90° -60° =30°, angle of refraction =? and η = 1.33
Thus;
Sin 30 / Sin r = 1.33
Sin r = Sin 30°/1.33
= 0.3759
r = Sin^-1 0.3759
= 22.08
<u>≈ 22°</u>
<h2>
Answer: 117.626m/s</h2>
Explanation:
The escape velocity 
is given by the following equation:
(1)
Where:
is the Gravitational Constant and its value is 
is the mass of the asteroid
is the radius of the asteroid
On the other hand, we know the density of the asteroid is 
and its volume is 
.
The density of a body is given by:
(2)
Finding :
(3)
(4) This is the mass of the spherical asteroid
In addition, we know the volume of a sphere is given by the following formula:
(5)
Finding :
![R=\sqrt[3]{\frac{3V}{4\pi}}](https://tex.z-dn.net/?f=R%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B3V%7D%7B4%5Cpi%7D%7D)
(6)
![R=\sqrt[3]{\frac{3(2.17(10)^{12}m^{3})}{4\pi}}](https://tex.z-dn.net/?f=R%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B3%282.17%2810%29%5E%7B12%7Dm%5E%7B3%7D%29%7D%7B4%5Cpi%7D%7D)
(7)
(8) This is the radius of the asteroid
Now we have all the necessary elements to calculate the escape velocity from (1):
(9)
Finally:
This is the minimum initial speed the rocks need to be thrown in order for them never return back to the asteroid.
Explanation:
According to Dalton's atomic theory, all the atoms are individual, all the atoms of the same element are identical in properties and mass, the compound is formed from two or more kinds of the atoms, all the matter is made up of small atoms and the chemical reaction is a rearrangement of the atoms.
The discoveries which contradicts the components of Dalton's atomic theory from the given discoveries are:
Nuclear reactions can change an atom of one element into an atom of another element.
Atoms of a given element can have different numbers of neutrons.
Atoms contain smaller particles: protons, neutrons, and electrons.
