Question

An earthquake emits both S-waves and P-waves which travel at different speeds through the Earth. A P-wave travels at 9000 m/s and an S-wave travels at 5000 m/s. If P-waves are received at a seismic station 2.00 minute before an S wave arrives, how far away is the earthquake center?

Answer 1

Answer:

the distance is 1350 Km

Explanation:

To solve this problem we will use the formulas of contant velocity motion:

$d=v*t\\where:\\d=distance\\v=velocity\\t=time$

Because the waves have to travel the same distance we can set the following equallity:

$vs*ts=vp*tp$

We know that the s waves arrive 2 minutes later, that is 120 seconds:

$vs*(120+t1)=vp*t1$

Rearranging the last equation we have :

$t1=120*\frac{vs}{vp-vs}\\\\t1=120*\frac{5000}{9000-5000}\\\\t1=150seconds$

As we said before they have to travel the same distance, so:

$d=9000(\frac{m}{s})*150(s)\\d=1350000(m)\\d=1350(km)$