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!!!!!!!

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.

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

To find the wave energy per square foot when the wind speed is 20 knots, we can use the given equation: E = 0.002888s^4, where s is the wind speed in knots.

Substituting s = 20 into the equation, we get:
E = 0.002888 * (20^4)
E = 0.002888 * (160,000)
E ≈ 462.08 foot pounds

Therefore, the wave energy per square foot when the wind speed is 20 knots is approximately 462.08 foot pounds.

To find the wave energy per square foot when the wind speed is 40 knots, we can again use the equation:
E = 0.002888s^4

Substituting s = 40 into the equation, we get:
E = 0.002888 * (40^4)
E = 0.002888 * (1,600,000)
E ≈ 4,611.2 foot pounds

Therefore, the wave energy per square foot when the wind speed is 40 knots is approximately 4,611.2 foot pounds.

Now, let's compare the wave energy for a 40 knot wind to that of a 20 knot wind:
E(40 knots) / E(20 knots) ≈ 4,611.2 / 462.08
≈ 9.997

The ratio of wave energy for a 40 knot wind to that of a 20 knot wind is approximately 9.997, which is almost 10.

Hence, the wave energy for a 40 knot wind is roughly 10 times (not 17 times) the wave energy for a 20 knot wind.