Answer:9.75 m/s
Explanation:
Given
Length of ladder ![(L)=5 m](https://tex.z-dn.net/?f=%28L%29%3D5%20m)
Foot the ladder is moving away with speed of ![\frac{\mathrm{d} x}{\mathrm{d} t}=13 m/s](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cmathrm%7Bd%7D%20x%7D%7B%5Cmathrm%7Bd%7D%20t%7D%3D13%20m%2Fs)
From diagram
------1
at ![x=3](https://tex.z-dn.net/?f=x%3D3%20)
![y^2=25-9=16](https://tex.z-dn.net/?f=y%5E2%3D25-9%3D16)
![y=4 m](https://tex.z-dn.net/?f=y%3D4%20m)
Now differentiating equation 1 w.r.t time
![2x\frac{\mathrm{d} x}{\mathrm{d} t}+2y\frac{\mathrm{d} y}{\mathrm{d} t}=0](https://tex.z-dn.net/?f=2x%5Cfrac%7B%5Cmathrm%7Bd%7D%20x%7D%7B%5Cmathrm%7Bd%7D%20t%7D%2B2y%5Cfrac%7B%5Cmathrm%7Bd%7D%20y%7D%7B%5Cmathrm%7Bd%7D%20t%7D%3D0)
![x\frac{\mathrm{d} x}{\mathrm{d} t}=-y\frac{\mathrm{d} y}{\mathrm{d} t}](https://tex.z-dn.net/?f=x%5Cfrac%7B%5Cmathrm%7Bd%7D%20x%7D%7B%5Cmathrm%7Bd%7D%20t%7D%3D-y%5Cfrac%7B%5Cmathrm%7Bd%7D%20y%7D%7B%5Cmathrm%7Bd%7D%20t%7D)
![3\times 13=-4\times \frac{\mathrm{d} y}{\mathrm{d} t}](https://tex.z-dn.net/?f=3%5Ctimes%2013%3D-4%5Ctimes%20%5Cfrac%7B%5Cmathrm%7Bd%7D%20y%7D%7B%5Cmathrm%7Bd%7D%20t%7D)
![\frac{\mathrm{d} y}{\mathrm{d} t}=-\frac{3\times 13}{4}=-9.75 m/s](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cmathrm%7Bd%7D%20y%7D%7B%5Cmathrm%7Bd%7D%20t%7D%3D-%5Cfrac%7B3%5Ctimes%2013%7D%7B4%7D%3D-9.75%20m%2Fs)
negative indicates distance is decreasing with time
A globe sitting on the desk can't demonstrate the speed of axial rotation
or the speed of orbital revolution.
Answer:
The differences between the Lincoln, Johnson, and Congress Reconstruction plans include: Although both the Lincoln and Johnson plan were open to readmission of the southern States, Congress claimed that the two administrations were too lenient and sought stiffer punishment for the States
The aspect of Abraham Lincoln's plan for reconstruction in the South that made it differ from the plan of congressional leaders was that Lincoln's plan was more focused on helping the South rebuild than on punishing it and the Radical Republicans' reconstruction offered all kinds of new opportunities to African Americans, including the vote (for males), property ownership, education, legal rights, and even the possibility of holding political office. By the beginning of 1868, about 700,000 African Americans were registered voters.
Reconstruction encompassed three major initiatives:
1. restoration of the Union
2. transformation of southern society
3.enactment of progressive legislation favoring the rights of freed slaves
Answer:
When the air pressure in the throat and outside the body is less than the air pressure in the middle ear, barotrauma occurs.
Explanation:
Ear barotrauma is a medical condition that describes discomfort in the ear which is caused by pressure differences in the inner and outer ear drum.
Usually, the air pressure in the middle ear is the same as the air pressure in the throat and outside the body.
When we swallow, the eustachian tube opens up and air flows out of and into the middle ear, this balances the pressure. But if the eustachian tube is blocked, the air pressure in the throat and outer body become different from the air pressure in the middle ear.
To solve this problem it is necessary to apply the concepts related to the conservation of the Gravitational Force and the centripetal force by equilibrium,
![F_g = F_c](https://tex.z-dn.net/?f=F_g%20%3D%20F_c)
![\frac{GmM}{r^2} = \frac{mv^2}{r}](https://tex.z-dn.net/?f=%5Cfrac%7BGmM%7D%7Br%5E2%7D%20%3D%20%5Cfrac%7Bmv%5E2%7D%7Br%7D)
Where,
m = Mass of spacecraft
M = Mass of Earth
r = Radius (Orbit)
G = Gravitational Universal Music
v = Velocity
Re-arrange to find the velocity
![\frac{GM}{r^2} = \frac{v^2}{r}](https://tex.z-dn.net/?f=%5Cfrac%7BGM%7D%7Br%5E2%7D%20%3D%20%5Cfrac%7Bv%5E2%7D%7Br%7D)
![\frac{GM}{r} = v^2](https://tex.z-dn.net/?f=%5Cfrac%7BGM%7D%7Br%7D%20%3D%20v%5E2)
![v = \sqrt{\frac{GM}{r}}](https://tex.z-dn.net/?f=v%20%3D%20%5Csqrt%7B%5Cfrac%7BGM%7D%7Br%7D%7D)
PART A ) The radius of the spacecraft's orbit is 2 times the radius of the earth, that is, considering the center of the earth, the spacecraft is 3 times at that distance. Replacing then,
![v = \sqrt{\frac{(6.67*10^{-11})(5.97*10^{24})}{3*(6.371*10^6)}}](https://tex.z-dn.net/?f=v%20%3D%20%5Csqrt%7B%5Cfrac%7B%286.67%2A10%5E%7B-11%7D%29%285.97%2A10%5E%7B24%7D%29%7D%7B3%2A%286.371%2A10%5E6%29%7D%7D)
![v = 4564.42m/s](https://tex.z-dn.net/?f=v%20%3D%204564.42m%2Fs)
From the speed it is possible to use find the formula, so
![T = \frac{2\pi r}{v}](https://tex.z-dn.net/?f=T%20%3D%20%5Cfrac%7B2%5Cpi%20r%7D%7Bv%7D)
![T = \frac{2\pi (6.371*10^6)}{4564.42}](https://tex.z-dn.net/?f=T%20%3D%20%5Cfrac%7B2%5Cpi%20%286.371%2A10%5E6%29%7D%7B4564.42%7D)
![T = 8770.05s\approx 146min\approx 2.4hour](https://tex.z-dn.net/?f=T%20%3D%208770.05s%5Capprox%20146min%5Capprox%202.4hour)
Therefore the orbital period of the spacecraft is 2 hours and 24 minutes.
PART B) To find the kinetic energy we simply apply the definition of kinetic energy on the ship, which is
![KE = \frac{1}{2} mv^2](https://tex.z-dn.net/?f=KE%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20mv%5E2)
![KE = \frac{1}{2} (100)(4564.42)^2](https://tex.z-dn.net/?f=KE%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%28100%29%284564.42%29%5E2)
![KE = 1.0416*10^9J](https://tex.z-dn.net/?f=KE%20%3D%201.0416%2A10%5E9J)
Therefore the kinetic energy of the Spacecraft is 1.04 Gigajules.