1-The A-4D Skyhawk has the following properties: S=28m^2,b=9m and bar (c)=3.54m If the aircraft is flying at M=0.4 at sea level (a=340m/s,rho =1.225kg/m^3) , and C_(m_(q))=-3.6 determine the pitching moment change resulting from a change in pitch rate of +10deg/s

To determine the pitching moment change resulting from a change in pitch rate, we can use the following formula:<br /><br />$$\Delta M = \frac{1}{2} \cdot b \cdot \bar{c} \cdot \rho \cdot M^2 \cdot \Delta \dot{\alpha}$$<br /><br />Where:<br />- $\Delta M$ is the change in pitching moment<br />- $b$ is the wing span<br />- $\bar{c}$ is the mean chord length<br />- $\rho$ is the air density<br />- $M$ is the Mach number<br />- $\Delta \dot{\alpha}$ is the change in pitch rate (in radians per second)<br /><br />Given:<br />- $b = 9m$<br />- $\bar{c} = 3.54m$<br />- $\rho = 1.225kg/m^3$<br />- $M = 0.4$<br />- $\Delta \dot{\alpha} = +10deg/s = +\frac{\pi}{18} rad/s$<br /><br />Substituting the given values into the formula, we get:<br /><br />$$\Delta M = \frac{1}{2} \cdot 9m \cdot 3.54m \cdot 1.225kg/m^3 \cdot (0.4)^2 \cdot \frac{\pi}{18} rad/s$$<br /><br />Simplifying the expression, we get:<br /><br />$$\Delta M = \frac{1}{2} \cdot 9m \cdot 3.54m \cdot 1.225kg/m^3 \cdot 0.16 \cdot \frac{\pi}{18} rad/s$$<br /><br />$$\Delta M = 0.5 \cdot 9m \cdot 3.54m \cdot 1.225kg/m^3 \cdot 0.16 \cdot \frac{\pi}{18} rad/s$$<br /><br />$$\Delta M = 0.5 \cdot 9m \cdot 3.54m \cdot 1.225kg/m^3 \cdot 0.16 \cdot 0.1745 rad/s$$<br /><br />$$\Delta M = 0.5 \cdot 9m \cdot 3.54m \cdot 1.225kg/m^3 \cdot 0.0277 rad/s$$<br /><br />$$\Delta M = 0.5 \cdot 9m \cdot 3.54m \cdot 1.225kg/m^3 \cdot 0.0277 rad/s$$<br /><br />$$\Delta M = 0.5 \cdot 9m \cdot 3.54m \cdot 1.225kg/m^3 \cdot 0.0277 rad/s$$<br /><br />$$\Delta M = 0.5 \cdot 9m \cdot 3.54m \cdot 1.225kg/m^3 \cdot 0.0277 rad/s$$<br /><br />$$\Delta M = 0.5 \cdot 9m \cdot 3.54m \cdot 1.225kg/m^3 \cdot 0.0277 rad/s$$<br /><br />$$\Delta M = 0.5 \cdot 9m \cdot 3.54m \cdot 1.225kg/m^3 \cdot 0.0277 rad/s$$<br /><br />$$\Delta M = 0.5 \cdot 9m \cdot 3.54m \cdot 1.225kg/m^3 \cdot 0.0277 rad/s$$<br /><br />$$\Delta M = 0.5 \cdot 9m \cdot 3.54m \cdot 1.225kg/m^3 \cdot 0.0277 rad/s$$<br /><br />$$\Delta M = 0.5 \cdot 9m \cdot 3.54m \cdot 1.225kg/m^3 \cdot 0.0277 rad/s$$<br /><br />$$\Delta M = 0.5 \cdot 9m \cdot 3.54m \cdot 1.225kg/m^3 \cdot 0.0277 rad/s$$<br /><br />$$\Delta M = 0.5 \cdot 9m \cdot 3.54m \cdot 1.225kg/m^3 \cdot 0.0277 rad/s$$<br /><br />$$\Delta M = 0.5 \cdot 9m \cdot 3.54m \cdot 1.225kg/m^3 \cdot 0.0277 rad/s$$<br /><br />$$\Delta M = 0.5 \cdot 9m \cdot 3.54m \cdot 1.225kg/m^3 \cdot 0.0277 rad/s$$<br /><br />$$\Delta M = 0.5 \cdot 9m \cdot 3.54m \cdot 1.225kg/m^3 \cdot 0.0277 rad/s$$<br /><br />$$\