An earthquake generates three kinds of waves: surface waves (L waves), which are the slowest and weakest; shear (S) waves, which are transverse waves and carry most of the energy; and pressure (P) waves, which are longitudinal waves and travel the fastest. The speed of P waves is approximately 7.0 km/s, and that of S waves is about 4.0 km/s. Animals seem to feel the P waves. If a dog senses the arrival of P waves and starts barking 23.3 s before an earthquake is felt by humans, approximately how far is the dog from the earthquake’s epicenter?

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To determine the distance between the dog and the earthquake's epicenter, we need to utilize the speed of the waves and the time difference between when the dog senses the P waves and when humans feel the earthquake.

Given:
Speed of P waves (vP) = 7.0 km/s
Time difference (t) = 23.3 s

We know that distance (d) can be calculated using the formula: distance = speed × time.

Let's calculate the distance traveled by the P waves before humans felt the earthquake:

Distance traveled by P waves = vP × t
= 7.0 km/s × 23.3 s
= 162.1 km

Therefore, the dog is approximately 162.1 km away from the earthquake's epicenter.