Offshore wind turbines are useful because a. they do not need gearboxes. b. they are easier to build than wind turbines on land. c. average wind speeds are greater over water than land. d. they do not require a generator to produce electricity.

Weather The function $w=-39+\frac{3}{2} t$, where $t$ is the actual air temperature, gives the approximate wind chill temperature $w$ when the wind speed is 20 $\mathrm{mi} / \mathrm{h}$. Find the approximate wind chill temperature for the given air temperatures with a $20 \mathrm{mi} / \mathrm{h}$ wind. c. $-8^{\circ} \mathrm{F}$

The wind chill temperature in degrees is a function of the air temperature T (in degrees Fahrenheit) and the wind speed v (in mi/h). If we hold T constant and consider the wind chill as a function of v, we have

$$w(v)=\left\{\begin{array}{ll}{T} & {\text { if } 0 \leq v \leq 4} \\ {91.4+(91.4-T)\\(0.0203 v- \\0.304 \sqrt{v} \cdot 0.474)} & {\text { if } 4<v<45} \\ {1.6 T-55} & {\text { if } v \geq 45}\end{array}\right.$$

(a.) If T = 30, what is the wind chill for v = 20? What is it for v = 50? (b.) For T = 30, what wind speed corresponds to a wind chill temperature of $0^{\circ}$? (c.) For what value of T is the wind chill function continuous at v = 4$ At v = 45?

Weather The function $w=-39+\frac{3}{2} t$, where $t$ is the actual air temperature, gives the approximate wind chill temperature $w$ when the wind speed is 20 $\mathrm{mi} / \mathrm{h}$. Find the approximate wind chill temperature for the given air temperatures with a $20 \mathrm{mi} / \mathrm{h}$ wind. b. $-24^{\circ} \mathrm{F}$

Two wind turbines generate a total of 57 kW of power. The larger turbine generates twice as much power as the smaller one. Find the power output of each turbine.

Wind-powered energy The cubic polynomial function provides the power $P$, in watts, produced by a specific wind turbine with winds blowing at $v$ meters per second.

$$P(v)=4.95 v^3$$

What happens to the power produced by the turbine if the wind speed doubles?

With a tail wind, a small Piper aircraft can fly 600 miles in 3 hours. Against this same wind, the Piper can fly the same distance in 4 hours. Find the average wind speed and the average airspeed of the Piper.

What is the solar wind?

Make a scatterplot of the data and draw a line of best fit. Then use the data to predict the wind chill at 35 mi/h.

apparent Temperature Due to Wind at 1$^{\circ}$F Wind speed (mi/h): 10, 20, 30, 40, 50, 60 Wind chill ($^{\circ}$F): 2.7, -2.3, -5.5, -7.9, -9.8, -11.4

Flying with the wind, a plane flew 1000 miles in 5 hours. Flying against the wind, the plane could fly only 500 miles in the same amount of time. Find the speed of the plane in calm air and the speed of the wind.

What causes wind?

A plane that can fly 200 mph in still air makes a 330-mile flight with a tail wind and returns, flying into the same wind. Find the speed of the wind if the total flying time is

$$3 \frac { 1 } { 3 }$$

hours.

Wind-powered energy The cubic polynomial function provides the power $P$, in watts, produced by a specific wind turbine with winds blowing at $v$ meters per second.

$$P(v)=4.95 v^3$$

What happens to the power produced by the turbine if the wind speed is tripled?

A plane flew $1750 \mathrm{~km}$ in $6 \mathrm{~h}$ with a tail wind of constant velocity. It then flew back $540 \mathrm{~km}$ in $3 \mathrm{~h}$ with a head wind of the same velocity. Find the speed of the plane and the speed of the wind.