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Oceanography Practice Problems
The following pages contain numerical word
problems presented in lecture. There are two
steps to solving word problems :
1) translate the wording into a numeric
equation;
– What are the variables, constants (for
example, distance (d), rate ( r)
2) solve the equation!
– This may first involve simplying the
equation (combining like terms, etc)
Problem #1: Computing Longitude
You are in the Pacific Ocean after having sailed from Santa Cruz 4
days earlier. It is noon (12:00) on the ship (local time), but a clock
that keeps Santa Cruz time is at 3 PM (15:00).
How many degrees of longitude have you traveled relative to Santa
Cruz?
Recall: 360° longitude / 24 hr = 15°/hr
Solution:
• 15:00-12:00=3 hr
• 3 hr x 15°/hr = 45°
You are 45° to the west
Problem #2: Water Depth
You are in the Atlantic Ocean measuring water depth using sonar.
The sonar records two way travel time (from ship to seafloor and
back) of 3 seconds. Assuming that the average velocity of sound in
seawater is 1.5 km/sec, determine the water depth in meters.
Solution:
d = r x t, r=1.5 km/sec, t=3 sec
d =1.5 km/sec x 3 sec = 4.5 km
4.5 km/2 = 2.25 km
2.25 km x 1000 m/km = 2250 m
Problem #3: Computing Distance to Epi-center
What do we know?
VP = 8 km/sec, VS = 4 km/sec
• Difference in arrival time (∆T) between p and s waves = TS - T P
Time it takes p and s waves to travel the same distance (D)
• TP = D/8 , TS = D/4
∆T between the P- waves and S-waves is:
• ∆T = TS - T P = D/4 – D/8 = 2D/8 - D/8
or
• ∆T = D/8
The distance D from the earthquake epicenter to seismic station is:
• D = 8 ∆T (constant is generally closer to 6)
Example: S arrives 10 sec after P
D = 8 ∆T = 8 km/sec (10 sec) = 80 km