By using the orbital period equation we will find that the orbital radius is r = 4.29*10^11 m
<h3>
What is the orbital period?</h3>
This would be the time that a given body does a complete revolution in its orbit.
It can be written as:
Where:
- π = 3.14
- G is the gravitational constant = 6.67*10^(-11) m^3/(kg*s^2)
- M is the mass of the sun = 1.989*10^30 kg
- r is the radius, which we want to find.
Rewriting the equation for the radius we get:
![T = \sqrt{\frac{4*\pi ^2*r^3}{G*M} }\\\\r = \sqrt[3]{ \frac{T^2*G*M}{4*\pi ^2} }](https://tex.z-dn.net/?f=T%20%3D%20%5Csqrt%7B%5Cfrac%7B4%2A%5Cpi%20%5E2%2Ar%5E3%7D%7BG%2AM%7D%20%7D%5C%5C%5C%5Cr%20%3D%20%5Csqrt%5B3%5D%7B%20%5Cfrac%7BT%5E2%2AG%2AM%7D%7B4%2A%5Cpi%20%5E2%7D%20%7D)
Where T = 7.5 years = 7.5*(3.154*10^7 s) = 2.3655*10^8 s
Replacing the values in the equation we get:
![r = \sqrt[3]{ \frac{(2.3655*10^8 s)^2*(6.67*10^{-11} m^3/(kg*s^2))*(1.989*10^{30} kg)}{4*3.14 ^2} } = 4.29*10^{11 }m](https://tex.z-dn.net/?f=r%20%3D%20%5Csqrt%5B3%5D%7B%20%5Cfrac%7B%282.3655%2A10%5E8%20s%29%5E2%2A%286.67%2A10%5E%7B-11%7D%20m%5E3%2F%28kg%2As%5E2%29%29%2A%281.989%2A10%5E%7B30%7D%20kg%29%7D%7B4%2A3.14%20%5E2%7D%20%7D%20%3D%204.29%2A10%5E%7B11%20%7Dm)
So the orbital radius is 4.29*10^11 m
If you want to learn more about orbits, you can read:
brainly.com/question/11996385
All cops are brave. And what’s the full question?
Answer:
a) The maximum height the ball will achieve above the launch point is 0.2 m.
b) The minimum velocity with which the ball must be launched is 4.43 m/s or 0.174 in/ms.
Explanation:
a)
For the height reached, we use 3rd equation of motion:
2gh = Vf² - Vo²
Here,
Vo = 3.75 m/s
Vf = 0m/s, since ball stops at the highest point
g = -9.8 m/s² (negative sign for upward motion)
h = maximum height reached by ball
therefore, eqn becomes:
2(-9.8m/s²)(h) = (0 m/s)² - (3.75 m/s²)²
<u>h = 0.2 m</u>
b)
To find out the initial speed to reach the hoop at height of 3.5 m, we again use 3rd eqn. of motion with h= 3.5 m - 2.5m = 1 m (taking launch point as reference), and Vo as unknown:
2(-9.8m/s²)(1 m) = (0 m/s)² - (Vo)²
(Vo)² = 19.6 m²/s²
Vo = √19.6 m²/s²
<u>Vo = 4.43 m/s</u>
Vo = (4.43 m/s)(1 s/1000 ms)(39.37 in/1 m)
<u>Vo = 0.174 in/ms</u>
<u />
Easy ! EVERY element and every compound melts, then boils and becomes a gas, if you heat it to a high enough temperature. That includes iron, gold, water, salt, glass, almost any substance.
The one that's completely submerged is displacing more water, so the buoyant force on it is greater.
