Answer:
![v_{p}=647.72\frac{km}{s}](https://tex.z-dn.net/?f=v_%7Bp%7D%3D647.72%5Cfrac%7Bkm%7D%7Bs%7D)
Explanation:
According to Kepler's second law: a line segment joining an object and the Sun sweeps out equal areas during equal intervals of time. This law is equivalent to the constancy of the angular momentum, that is to say:
![\Delta \vec{L}=0\\\vec{L}_{p}=\vec{L}_{a}\\m*(\vec{r}_{p}\times \vec{v}_{p})=m*(\vec{r}_{a}\times \vec{v}_{a})\\mr_{p} v_{p}sin (\theta)=mr_{a} v_{a}sin (\theta)](https://tex.z-dn.net/?f=%5CDelta%20%5Cvec%7BL%7D%3D0%5C%5C%5Cvec%7BL%7D_%7Bp%7D%3D%5Cvec%7BL%7D_%7Ba%7D%5C%5Cm%2A%28%5Cvec%7Br%7D_%7Bp%7D%5Ctimes%20%5Cvec%7Bv%7D_%7Bp%7D%29%3Dm%2A%28%5Cvec%7Br%7D_%7Ba%7D%5Ctimes%20%5Cvec%7Bv%7D_%7Ba%7D%29%5C%5Cmr_%7Bp%7D%20v_%7Bp%7Dsin%20%28%5Ctheta%29%3Dmr_%7Ba%7D%20v_%7Ba%7Dsin%20%28%5Ctheta%29)
Here,
is the comet's mass,
is its distance from the Sun,
is its speed and
the angle between
and
The aphelion and the perihelion are the only two points in the orbit where the radius and velocity are perpendicular. Therefore, at these 2 points, the angular momentum module can be calculated as a simple product:
![mr_{p} v_{p}sin (^\circ 90)=mr_{a} v_{a}sin (^\circ 90)\\mr_{p} v_{p}=mr_{a} v_{a}](https://tex.z-dn.net/?f=mr_%7Bp%7D%20v_%7Bp%7Dsin%20%28%5E%5Ccirc%2090%29%3Dmr_%7Ba%7D%20v_%7Ba%7Dsin%20%28%5E%5Ccirc%2090%29%5C%5Cmr_%7Bp%7D%20v_%7Bp%7D%3Dmr_%7Ba%7D%20v_%7Ba%7D)
Rewriting for
:
![v_{p}=\frac{r_{a}v_{a}}{r_{p}}\\v_{p}=\frac{(5.7*10^{12}m)10\frac{km}{s}}{8.8*10^{10}m}\\v_{p}=647.72\frac{km}{s}](https://tex.z-dn.net/?f=v_%7Bp%7D%3D%5Cfrac%7Br_%7Ba%7Dv_%7Ba%7D%7D%7Br_%7Bp%7D%7D%5C%5Cv_%7Bp%7D%3D%5Cfrac%7B%285.7%2A10%5E%7B12%7Dm%2910%5Cfrac%7Bkm%7D%7Bs%7D%7D%7B8.8%2A10%5E%7B10%7Dm%7D%5C%5Cv_%7Bp%7D%3D647.72%5Cfrac%7Bkm%7D%7Bs%7D)
Ignoring air resistance, the fall has no effect on its horizontal speed. Traveling horizontally at 150 m/s for 25 seconds, it'll cover
(25) x (150m) = 3,750 meters
(about 2.3 miles)
I believe the right answer choice is letter B
The vibrations are analyze and turned into sounds in you ear