Answer:
9090 m, 104 s
Explanation:
After the acceleration phase, the rocket reaches a height of:
x = x₀ + v₀ t + ½ at²
x = (0 m) + (0 m/s) (30 s) + ½ (10 m/s²) (30 s)²
x = 4500 m
And it reaches a velocity of:
v = at + v₀
v = (10 m/s²) (30 s) + (0 m/s)
v = 300 m/s
After the fuel runs out, the rocket goes into free fall. The maximum height reached is:
v² = v₀² + 2a(x - x₀)
(0 m/s)² = (300 m/s)² + 2(-9.8 m/s²)(x - 4500 m)
x ≈ 9090 m
The time to reach maximum height during free fall:
v = at + v₀
0 m/s = (-9.8 m/s²) t + (300 m/s)
t ≈ 30.6 s
And the time to land from the maximum height:
x = x₀ + v₀ t + ½ at²
0 m = (9090 m) + (0 m/s) t + ½ (-9.8 m/s²) t²
t ≈ 43.1 s
So the total time is:
t = 30 s + 30.6 s + 43.1 s
t ≈ 104 seconds
Answer:
Explanation:
Given that,
The speed of the car is
Vc = 97m/s
The radius of circular path of the car is
Rc = 420m
We want to find the angle of roadway banked β?
To determine the angle of roadway banked, we will use the formula
tanβ = Vc² / Rc•g
Where Vc = 97m/s, Rc = 420m and
g = 9.8m/s²
Then
tanβ = 97² / (420 × 9.8)
tanβ = 2.28596
β = ArcTan ( 2.28596)
β = 66.37°
The railway banked at an angle of 66.37°
Answer:
Explanation:
The average energy of the system with quartic degrees of freedom. The quartic degrees of freedom is same as biquadratic since it means 4. Systems having quartic degrees of freedom are usually have their energies represented in terms of some variable raised to the power of 4.
The given system with quartic degrees of freedom here has E(x) = cx4 . The standard result from the statistical mechanics will be helpful here in calculating internal energy of the system, which is also its average energy.
U = kT^2\d(lnq)}/dT
Now, to find out q(x) we will use the equation q(x) = \int^{+\infty}_{-\infty} exp\bigg(\frac{-E(x)}{kT}\bigg)dx = \int^{+\infty}_{-\infty} exp\bigg(\frac{-cx^4}{kT}\bigg)dx
For a quadratic system, you would get a Gaussian integral which has a standard result.
A reaction between two pure solids is very rare. For a reaction to occur, the molecules must interact with each other. Since molecules of solids are very compact, they don't have the liberty to collide with one another. However, this is made possible by hydrates of solids. An examples would be CuSO₄·5H₂O. In this case, they have a an intermediate liquid to react them together.
Answer:
<em>Yes. Something similar occurs here on Earth.</em>
Explanation:
Gravity tends to pull objects perpendicularly to the ground. In space, the absence of this force means there is no compression on the spine due to gravity trying to pull it down. This means that astronauts undergo an increase in height in space.
Here on Earth, we experience gravity pull on our spine during the day. At night when we sleep, we lie down with our spine parallel to the ground, which means that our spine is no longer under compression from gravity force. The result is that we are a few centimetres taller in the morning when we wake up, than we are before going to bed at night. The increase is not much pronounced here on Earth because there is a repeated cycle of compression and decompression of our spine due to gravity, unlike when compared to that of astronauts that spend long duration in space, all the while without gravity forces on their spine
