Unfortunately for mariners, the total amount of wave energy in a storm doesnt depend on the first power of wind speed, but on the fourth power. The seas generated by forty knot wind arent twice as violent as those from a twenty knot wind, they are 17 times more violent. A ships crew watching the anemometer climbs even ten knots could be in great danger.

Question

Unfortunately for mariners, the total amount of wave energy  in a storm doesnt depend on the first power of wind speed, but on the fourth power.  The seas generated by forty  knot wind arent twice as violent as those from a twenty knot wind, they are 17 times more violent.  A ships crew watching the anemometer climbs even ten knots could be in great danger.

E stands for energy (in foot pounds)in each square foot of a wave with height h.

An equation that relates E and s(speed of knots)is 0.002888s^4

What is the wave energy per square foot when the wind speed is 20 knots? 40 knots? Is the wave energy for a 40 knot wind about 1[7 times the wave energy for a 20 knot wind?

PLEASE HELP ME!!!!!!!

Reiny · Answer

it is actually 16 times as strong exactly, and it can actually be done mentally

the first E is .002888(20)^4
the second E is .002888(40)^2
= .002888(2)^4(20)^4

this answer differs from the first one by 2^4 which is 16

You could of course on your calculator perform each of the calculations, then divide one by the other.
Guess what, you will get 16

so a speed of 40 knots has 16 times as much energy as a speed of 20 knots.

Mackenzie · Answer

why did you multiply the second E to the 2nd power and the first E to the 4th power?