Answer:
doppler shift's formula for source and receiver moving away from each other:
<em>λ'=λ°√(1+β/1-β)</em>
Explanation:
acceleration of spaceship=α=29.4m/s²
wavelength of sodium lamp=λ°=589nm
as the spaceship is moving away from earth so wavelength of earth should increase w.r.t increasing speed until it vanishes at λ'=700nm
using doppler shift's formula:
<em>λ'=λ°√(1+β/1-β)</em>
putting the values:
700nm=589nm√(1+β/1-β)
after simplifying:
<em>β=0.17</em>
by this we can say that speed at that time is: v=0.17c
to calculate velocity at an acceleration of a=29.4m/s²
we suppose that spaceship started from rest so,
<em>v=v₀+at</em>
where v₀=0
so<em> v=at</em>
as we want to calculate t so:-
<em>t=v/a</em> v=0.17c ,c=3x10⁸ ,a=29.4m/s²
putting values:
=0.17(3x10⁸m/s)/29.4m/s²
<em>t=1.73x10⁶</em>
We can use the formula of the moment of inertia given by:
![r\cdot F=I\alpha](https://tex.z-dn.net/?f=r%5Ccdot%20F%3DI%5Calpha)
Where:
r = Distance from the point about which the torque is being measured to the point where the force is applied
F = Force
I = Moment of inertia
α = Angular acceleration
So:
![\begin{gathered} r\cdot F=(-0.26\times314+290\times0.32)=92.8-81.64=11.16 \\ I=0.930 \\ so,_{\text{ }}solve_{\text{ }}for_{\text{ }}\alpha: \\ \alpha=\frac{r\cdot F}{I} \\ \alpha=\frac{11.16}{0.930} \\ \alpha=\frac{12rad}{s^2} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20r%5Ccdot%20F%3D%28-0.26%5Ctimes314%2B290%5Ctimes0.32%29%3D92.8-81.64%3D11.16%20%5C%5C%20I%3D0.930%20%5C%5C%20so%2C_%7B%5Ctext%7B%20%7D%7Dsolve_%7B%5Ctext%7B%20%7D%7Dfor_%7B%5Ctext%7B%20%7D%7D%5Calpha%3A%20%5C%5C%20%5Calpha%3D%5Cfrac%7Br%5Ccdot%20F%7D%7BI%7D%20%5C%5C%20%5Calpha%3D%5Cfrac%7B11.16%7D%7B0.930%7D%20%5C%5C%20%5Calpha%3D%5Cfrac%7B12rad%7D%7Bs%5E2%7D%20%5Cend%7Bgathered%7D)
Answer:
12 rad/s²
Any object that is launched as a projectile will lose speed and, as a result, altitude, as it travels through the air. The rate at which the object loses speed and altitude depends on the amount of force that way applied to it when it was launched. It is also dependent on the size and shape of the item. This is why something like, say, a football is much faster to fall to the ground than a bullet.
Full moon!
when Earth is exactly between the Moon and Sun, Earth's shadow falls upon the surface of the Moon, dimming it and sometimes turning the surface red over the course of a few hours.