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)
To solve this problem it is necessary to apply the concepts related to the geometry of a cylindrical tank and its respective definition.
The volume of a tank is given by
![V = \frac{\pi d^2}{4}h](https://tex.z-dn.net/?f=V%20%3D%20%5Cfrac%7B%5Cpi%20d%5E2%7D%7B4%7Dh)
Where
d = Diameter
h = Height
Considering that there are two stages, let's define the initial and final volume as,
![V_0 = \frac{\pi d^2}{4}H](https://tex.z-dn.net/?f=V_0%20%3D%20%5Cfrac%7B%5Cpi%20d%5E2%7D%7B4%7DH)
![V_f = \frac{\pi d^2}{4}h](https://tex.z-dn.net/?f=V_f%20%3D%20%5Cfrac%7B%5Cpi%20d%5E2%7D%7B4%7Dh)
We know as well by definition that
![1gal = 3.785*10^{-3}m^3](https://tex.z-dn.net/?f=1gal%20%3D%203.785%2A10%5E%7B-3%7Dm%5E3)
Then we have for the statement that
![V_f = V_0 -1gal](https://tex.z-dn.net/?f=V_f%20%3D%20V_0%20-1gal)
![V_f = V_0 - 3.785*10^{-3}](https://tex.z-dn.net/?f=V_f%20%3D%20V_0%20-%203.785%2A10%5E%7B-3%7D)
Replacing the previous data
![\frac{\pi d^2}{4}h = \frac{\pi d^2}{4}H- 3.785*10^{-3}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cpi%20d%5E2%7D%7B4%7Dh%20%3D%20%5Cfrac%7B%5Cpi%20d%5E2%7D%7B4%7DH-%203.785%2A10%5E%7B-3%7D)
![\frac{\pi (3.6)^2}{4}h = \frac{\pi (3.6)^2}{4}(2)- 3.785*10^{-3}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cpi%20%283.6%29%5E2%7D%7B4%7Dh%20%3D%20%5Cfrac%7B%5Cpi%20%283.6%29%5E2%7D%7B4%7D%282%29-%203.785%2A10%5E%7B-3%7D)
Solving to get h,
![h = 1.99963m](https://tex.z-dn.net/?f=h%20%3D%201.99963m)
Therefore the change is
![\Delta h = H-h](https://tex.z-dn.net/?f=%5CDelta%20h%20%3D%20H-h)
![\Delta h = 2- 1.99963](https://tex.z-dn.net/?f=%5CDelta%20h%20%3D%202-%201.99963)
![\Delta h = 3.7*10^{-4}m=0.37mm](https://tex.z-dn.net/?f=%5CDelta%20h%20%3D%203.7%2A10%5E%7B-4%7Dm%3D0.37mm)
Therefore te change in the height of the water in the tank is 0.37mm
This state of motionlessness occurs because all of the kinetic energy in the car is absorbed by the spring in the form of elastic potential energy. The mathematical representation is:
1/2 mv² = 1/2 kx²
25m = kx², where m is the mass of the cart, k is the spring constant and x is the spring's extension.
Answer:
True.
Explanation:
Don't turn wide to the left as you start the turn. A driver behind may think you are turning left and try to pass you on the right. You may crash into the other vehicle as you complete your turn.
Instead, slowly give yourself and others more time to avoid problems, keep the rear of the vehicle close to the curb. This will stop other drivers from passing you on the right. This is called (button Hook)
If you are driving a truck or bus that cannot make the right turn without swinging into the other lane, turn wide as you complete the turn.
4 blocks north because he is it not asking for north east