Answer:
Explanation:
From the given information:
Distance ![d_i = 4.8 \times 10^{10} \ m](https://tex.z-dn.net/?f=d_i%20%3D%204.8%20%5Ctimes%2010%5E%7B10%7D%20%5C%20m)
Speed of the comet ![V_i = 9.1 \times 10^{4} \ m/s](https://tex.z-dn.net/?f=V_i%20%3D%209.1%20%5Ctimes%2010%5E%7B4%7D%20%5C%20m%2Fs)
At distance ![d_2 = 6 \times 10^{12} \ m](https://tex.z-dn.net/?f=d_2%20%3D%206%20%5Ctimes%2010%5E%7B12%7D%20%5C%20m)
where;
mass of the sun = ![1.98 \times 10^{30}](https://tex.z-dn.net/?f=1.98%20%5Ctimes%2010%5E%7B30%7D)
![G = 6.67 \times 10^{-11}](https://tex.z-dn.net/?f=G%20%3D%206.67%20%5Ctimes%2010%5E%7B-11%7D)
To find the speed
:
Using the formula:
![E_f = E_i + W \\ \\ where; \ \ W = 0 \ \ \text{since work done by surrounding is zero (0)}](https://tex.z-dn.net/?f=E_f%20%3D%20E_i%20%2B%20W%20%5C%5C%20%5C%5C%20%20where%3B%20%5C%20%20%5C%20%20W%20%3D%200%20%20%5C%20%5C%20%20%5Ctext%7Bsince%20work%20done%20by%20surrounding%20is%20zero%20%280%29%7D)
![E_f = E_i + 0 \\ \\ K_f + U_f = K_i + U_i \\ \\ = \dfrac{1}{2}mV_f^2 + \dfrac{-GMm}{d^2} = \dfrac{1}{2}mV_i^2+ \dfrac{-GMm}{d_i} \\ \\ V_f = \sqrt{V_i^2 + 2 GM \Big [ \dfrac{1}{d_2}- \dfrac{1}{d_i}\Big ]}](https://tex.z-dn.net/?f=E_f%20%3D%20E_i%20%2B%200%20%5C%5C%20%5C%5C%20%20K_f%20%2B%20U_f%20%3D%20K_i%20%2B%20U_i%20%20%5C%5C%20%5C%5C%20%3D%20%5Cdfrac%7B1%7D%7B2%7DmV_f%5E2%20%2B%20%20%5Cdfrac%7B-GMm%7D%7Bd%5E2%7D%20%3D%20%20%5Cdfrac%7B1%7D%7B2%7DmV_i%5E2%2B%20%5Cdfrac%7B-GMm%7D%7Bd_i%7D%20%5C%5C%20%5C%5C%20V_f%20%3D%20%5Csqrt%7BV_i%5E2%20%2B%202%20GM%20%5CBig%20%5B%20%20%5Cdfrac%7B1%7D%7Bd_2%7D-%20%5Cdfrac%7B1%7D%7Bd_i%7D%5CBig%20%5D%7D)
![V_f = \sqrt{(9.1 \times 10^{4})^2 + 2 (6.67\times 10^{-11}) *(1.98 * 10^{30} ) \Big [ \dfrac{1}{6*10^{12}}- \dfrac{1}{4.8*10^{10}}\Big ]}](https://tex.z-dn.net/?f=V_f%20%3D%20%5Csqrt%7B%289.1%20%5Ctimes%2010%5E%7B4%7D%29%5E2%20%2B%202%20%286.67%5Ctimes%2010%5E%7B-11%7D%29%20%2A%281.98%20%2A%2010%5E%7B30%7D%20%29%20%5CBig%20%5B%20%20%5Cdfrac%7B1%7D%7B6%2A10%5E%7B12%7D%7D-%20%5Cdfrac%7B1%7D%7B4.8%2A10%5E%7B10%7D%7D%5CBig%20%5D%7D)
![\mathbf{V_f =53.125 \times 10^4 \ m/s}](https://tex.z-dn.net/?f=%5Cmathbf%7BV_f%20%3D53.125%20%5Ctimes%2010%5E4%20%5C%20m%2Fs%7D)
Answer:
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No, speed is not a vector. it is scalar.
because it doesn't need direction but need magnitude.
The astronaut would go the opposite direction due to Newton’s third law of -10N, -10N, -9N, -9N
Let me know if this helped you, please rank this was the brainlist answer if possible, thanks!
Answer:
≈ 2.1 R
Explanation:
The moment of inertia of the bodies can be calculated by the equation
I = ∫ r² dm
For bodies with symmetry this tabulated, the moment of inertia of the center of mass
Sphere
= 2/5 M R²
Spherical shell
= 2/3 M R²
The parallel axes theorem allows us to calculate the moment of inertia with respect to different axes, without knowing the moment of inertia of the center of mass
I =
+ M D²
Where M is the mass of the body and D is the distance from the center of mass to the axis of rotation
Let's start with the spherical shell, axis is along a diameter
D = 2R
Ic =
+ M D²
Ic = 2/3 MR² + M (2R)²
Ic = M R² (2/3 + 4)
Ic = 14/3 M R²
The sphere
Is =
+ M [
²
Is = Ic
2/5 MR² + M
² = 14/3 MR²
² = R² (14/3 - 2/5)
= √ (R² (64/15)
= 2,066 R