Answer:
psychology has to do with the mind and brain while social science has to do with the scientific study if human relationships
Scientists measure the time between the arrival of an earthquake's __P____ and ___S____ waves to help determine the distance between the recording seismograph and the earthquake epicenter.
Explanation:
P- (compressional) and S- (shear) waves produced in earthquakes travel at different speeds. P waves are faster than S waves and hence will be detected first by a seismograph after an earthquake. The further away a seismograph is from the epicenter of an earthquake, the longer the time difference between the two (2) waves will be.
Using several, at least 3, seismographs located at different geoghraphical locations and detecting earthquakes, geologists can extrapolate the epicenter of an earthquake using the time differences in arrivals of the two waves in each of the seismographs, using the mathematics of triangulation.
Learn More:
For more on P- and S-- waves check out;
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Solution :
We know that :
Formula for Gravitational force is given by :
![$F_g=\frac{Gmn}{r^2}$](https://tex.z-dn.net/?f=%24F_g%3D%5Cfrac%7BGmn%7D%7Br%5E2%7D%24)
where, G is the gravitational constant
M is the mass of the bigger body
m is the mass of the smaller body
r is the distance between the two bodies.
And the formula for the centripetal force is given by :
![$F_c=\frac{mv^2}{r}$](https://tex.z-dn.net/?f=%24F_c%3D%5Cfrac%7Bmv%5E2%7D%7Br%7D%24)
where, m is the mass of the rotating body
v is the velocity
r is the radius of rotation of the body.
We know that mathematically, the gravitational force is equal to the centripetal force of the body.
Therefore,
![$F_g=F_c$](https://tex.z-dn.net/?f=%24F_g%3DF_c%24)
![$\frac{GMm}{r^2}=\frac{mv^2}{r}$](https://tex.z-dn.net/?f=%24%5Cfrac%7BGMm%7D%7Br%5E2%7D%3D%5Cfrac%7Bmv%5E2%7D%7Br%7D%24)
![$\sqrt{\frac{GM}{r}}=v$](https://tex.z-dn.net/?f=%24%5Csqrt%7B%5Cfrac%7BGM%7D%7Br%7D%7D%3Dv%24)
Hence derived.