An earthquake releases two types of traveling seismic waves, called transverse and longitudinal waves. The average speed of the transverse and longitudinal waves in rock are 8.8 km/s and 5.9 km/s respectively. A seismograph records the arrival of the transverse waves 69 s before that of the longitudinal waves. Assuming the waves travel in straight lines, how far away is the center of the earthquake

1239.216 km

Explanation:

The speed of the transverse = 8.8km/s

The speed of the longitudinal = 5.9km/s

distance = speed x time,

8.8km/s x trans_time = 5.9km/s x long_time

8.8 / 5.9 = long_time / trans_time

1.49 = long_time / trans_time

long_time = 1.49 trans_time

the transverse wave was 69s faster than longitudinal,

trans_time - long_time = 69s

trans_time - 1.49trans_time  = 69s

0.49 trans_time = 69

trans_time = 69 / 0.49 = 140.82s

long_time = 140.82 - 69 = 71.82s

the distance of the earthquake;

distance = 8.8 x 140.82 = 1239.216 km

think about the oscillation of the toy shown in the video. when the toy is at the highest point of its motion, its velocity is zero and its acceleration is negative.