Vi = vf + ( a.t)
0 m/s (rest) = 80 m/s + (a.20s.-1)
a.20.-1= -80, we check if this is true; = 0 m/s= 80 + -80 = 0 ITS TRUE.
so a.20.-1= -80, a= 80/20 , Answers a= 4 m/s
Answer:B
Explanation:
Given
Distance of astronaut From asteroid x is ![r_x=140 km](https://tex.z-dn.net/?f=r_x%3D140%20km)
Distance of astronaut From asteroid Y is ![r_y=581 km](https://tex.z-dn.net/?f=r_y%3D581%20km)
Suppose M,M_x,M_y be the masses of Astronaut , asteroid X and Y
If the astronaut is in equilibrium then net gravitational force on it is zero
![F_x=F_y](https://tex.z-dn.net/?f=F_x%3DF_y)
![\frac{GMM_x}{r_x^2}=\frac{GMM_y}{r_y^2}](https://tex.z-dn.net/?f=%5Cfrac%7BGMM_x%7D%7Br_x%5E2%7D%3D%5Cfrac%7BGMM_y%7D%7Br_y%5E2%7D)
cancel out the common terms we get
![\frac{M_x}{r_x^2}=\frac{M_y}{r_y^2}](https://tex.z-dn.net/?f=%5Cfrac%7BM_x%7D%7Br_x%5E2%7D%3D%5Cfrac%7BM_y%7D%7Br_y%5E2%7D)
![\frac{M_x}{M_y}=(\frac{r_x}{r_y})^2](https://tex.z-dn.net/?f=%5Cfrac%7BM_x%7D%7BM_y%7D%3D%28%5Cfrac%7Br_x%7D%7Br_y%7D%29%5E2)
![\frac{M_x}{M_y}=(\frac{140}{581})^2](https://tex.z-dn.net/?f=%5Cfrac%7BM_x%7D%7BM_y%7D%3D%28%5Cfrac%7B140%7D%7B581%7D%29%5E2)
![\frac{M_x}{M_y}=0.05806\approx 0.0581](https://tex.z-dn.net/?f=%5Cfrac%7BM_x%7D%7BM_y%7D%3D0.05806%5Capprox%200.0581)
1) 0.0011 rad/s
2) 7667 m/s
Explanation:
1)
The angular velocity of an object in circular motion is equal to the rate of change of its angular position. Mathematically:
![\omega=\frac{\theta}{t}](https://tex.z-dn.net/?f=%5Comega%3D%5Cfrac%7B%5Ctheta%7D%7Bt%7D)
where
is the angular displacement of the object
t is the time elapsed
is the angular velocity
In this problem, the Hubble telescope completes an entire orbit in 95 minutes. The angle covered in one entire orbit is
rad
And the time taken is
![t=95 min \cdot 60 =5700 s](https://tex.z-dn.net/?f=t%3D95%20min%20%5Ccdot%2060%20%3D5700%20s)
Therefore, the angular velocity of the telescope is
![\omega=\frac{2\pi}{5700}=0.0011 rad/s](https://tex.z-dn.net/?f=%5Comega%3D%5Cfrac%7B2%5Cpi%7D%7B5700%7D%3D0.0011%20rad%2Fs)
2)
For an object in circular motion, the relationship between angular velocity and linear velocity is given by the equation
![v=\omega r](https://tex.z-dn.net/?f=v%3D%5Comega%20r)
where
v is the linear velocity
is the angular velocity
r is the radius of the circular orbit
In this problem:
is the angular velocity of the Hubble telescope
The telescope is at an altitude of
h = 600 km
over the Earth's surface, which has a radius of
R = 6370 km
So the actual radius of the Hubble's orbit is
![r=R+h=6370+600=6970 km = 6.97\cdot 10^6 m](https://tex.z-dn.net/?f=r%3DR%2Bh%3D6370%2B600%3D6970%20km%20%3D%206.97%5Ccdot%2010%5E6%20m)
Therefore, the linear velocity of the telescope is:
![v=\omega r=(0.0011)(6.97\cdot 10^6)=7667 m/s](https://tex.z-dn.net/?f=v%3D%5Comega%20r%3D%280.0011%29%286.97%5Ccdot%2010%5E6%29%3D7667%20m%2Fs)
The greater the mass the greater is inertia.
Is there information in the previous question which relates to this one?