Answer:
0.00461031264 m/s
Explanation:
G = Gravitational constant = 6.67 × 10⁻¹¹ m³/kgs²
M = Mass of the Earth = 6 × 10²⁴ kg
r = Distance between Earth and Sun = ![1.5\times 10^{11}\ m](https://tex.z-dn.net/?f=1.5%5Ctimes%2010%5E%7B11%7D%5C%20m)
t = Time taken = 3 days
Acceleration is given by
![a=\dfrac{GM}{r^2}\\\Rightarrow a=\dfrac{6.67\times 10^{-11}\times 6\times 10^{24}}{(1.5\times 10^{11})^2}\\\Rightarrow a=1.77867\times 10^{-8}\ m/s^2](https://tex.z-dn.net/?f=a%3D%5Cdfrac%7BGM%7D%7Br%5E2%7D%5C%5C%5CRightarrow%20a%3D%5Cdfrac%7B6.67%5Ctimes%2010%5E%7B-11%7D%5Ctimes%206%5Ctimes%2010%5E%7B24%7D%7D%7B%281.5%5Ctimes%2010%5E%7B11%7D%29%5E2%7D%5C%5C%5CRightarrow%20a%3D1.77867%5Ctimes%2010%5E%7B-8%7D%5C%20m%2Fs%5E2)
Velocity of the star
![v=u+at\\\Rightarrow v=0+1.77867\times 10^{-8}\times 3\times 24\times 60\times 60\\\Rightarrow v=0.00461031264\ m/s](https://tex.z-dn.net/?f=v%3Du%2Bat%5C%5C%5CRightarrow%20v%3D0%2B1.77867%5Ctimes%2010%5E%7B-8%7D%5Ctimes%203%5Ctimes%2024%5Ctimes%2060%5Ctimes%2060%5C%5C%5CRightarrow%20v%3D0.00461031264%5C%20m%2Fs)
The Sun's speed will be 0.00461031264 m/s
You want to know the difference between the two velocities, so you have to think 9 m/s - 2 m/s. The result is 7 m/s, the second option of your list. Hope that was helpful, have a great day!
Answer: 2.3m/s
Explanation:
mass-energy balance: ke(f) + pe(f) = ke(o) + pe(o)
since we are looking for the point at the bottom of the pendulum, thats the reference point, the lowest in the system. pe(f) is 0, since h
ke(f)=0.5m x v(f)^2
pe(f)=0
ke(o)=0.5m x v(o)^2
pe(o)-mxgxh
find h by: drawing a triangle with the pendulum at the vertical, then displaced by 25 degrees , The difference in height is h, because cos(25)=(adj)/(hyp)=(2-h)/2. I found h=0.187m
In the m-e balance, cancel the masses in all the terms.
.5xv(f)^2 =0.5v(o)^2 +gxh
Given v(o) = 1.2 m/s and g = 9.8 then v(f) = 2.2595 m/s
Therefore V(0) = 2.3 m/s