How Long Will It Take for Storm Waves to Reach Hawaii?

[YEAH!]

Homework Statement

A fierce winter storm blows across a large fetch of the South Pacific near the Antarctic. The waves it generates have a wavelength of 1500 feet with a 15-second period. They originate at a distance of 5000 miles from your favorite Hawaiian surfing beach. How many days will it take for these waves to arrive at your beach (so you know what day to call in sick to work and school)?

Homework Equations

C=L/T

C=speed (which is what I need to find)
L=wavelength
T=time or period per sec

The Attempt at a Solution

so the problem would setup like this? C=1500ft/15sec


3600 seconds in an hour
5280 feet in a mile.


1500 feet/sec = (1500 feet/sec) x (3600 sec/hr) = 5,400,000ft per hour

this is where I get lost so every hr the wave travels 5,400,000ft

 

[Redbelly98]

Welcome to PF.

Homework Equations

C=L/T

C=speed (which is what I need to find)
L=wavelength
T=time or period per sec

The Attempt at a Solution

so the problem would setup like this? C=1500ft/15sec

Yes. So C = ____ ft/sec?

3600 seconds in an hour
5280 feet in a mile.


1500 feet/sec = (1500 feet/sec) x (3600 sec/hr) = 5,400,000ft per hour

this is where I get lost so every hr the wave travels 5,400,000ft

The wave speed is not 1500 ft/sec. Other than that, your method of converting to ft/hour is correct. Now you have to convert that into miles/hour.

Hint: Multiply by either (5280 ft/mile), or by [ 1 mile / (5280 ft)]. Use the one that makes the units work out correctly.

 

[YEAH!]

Thanks for the welcome Redbelly98.

So in the case of my problem:
A wavelength of 1500 feet with a 15-second period, originating at a distance of 5000 miles from the destination.

the wave would travel 6000ft in 60 secs or 100ft/sec
(100 feet/sec) x (3600 sec/hr) = (360,000ft per hour) x (1 mile/5280 feet) or 360,000ft / 5280 = 68.181818181818182 mph so in order to find how many hours it would take to reach a beach 5,000miles away we simply divide again?
5000 / 68.181818181818182 = 73.3hrs or 3days and 1.3hrs?

 

[YEAH!]

If that's not right could you possibly help me out with a example using different numbers?

 

[Redbelly98]

A wavelength of 1500 feet with a 15-second period, originating at a distance of 5000 miles from the destination.

the wave would travel 6000ft in 60 secs or 100ft/sec
(100 feet/sec) x (3600 sec/hr) = (360,000ft per hour) x (1 mile/5280 feet) or 360,000ft / 5280 = 68.181818181818182 mph

so in order to find how many hours it would take to reach a beach 5,000miles away we simply divide again?
5000 / 68.181818181818182 = 73.3hrs or 3days and 1.3hrs?

Correct!