Chapter Project 679 1. Find the real solutions, if any, of the equation = − e 1 x 9 2 2. Find an equation for the line containing the origin that makes an angle of ° 30 with the positive x-axis. 3. Find an equation for the circle with center at the point ( ) 0, 1 and radius 3. Graph this circle. 4. What is the domain of the function ( ) ( ) = − f x x ln 1 2 ? 5. Test the equation + = x y x2 2 3 4 for symmetry with respect to the x-axis, the y-axis, and the origin. 6. Graph the function = y x ln . 7. Graph the function = y x sin . 8. Graph the function = y x sin . 9. Find the exact value of ( ) − − sin 1 2 . 1 10. Graph the equations = x 3 and = y 4 on the same set of rectangular coordinates. 11. Graph the equations = r 2 and θ π = 3 on the same set of polar coordinates. 12. What are the amplitude and period of π( ) = − y x 4cos ? Cumulative Review In 1903 the Wright brothers made the first controlled powered flight. The weight of their plane was approximately 700 pounds (lb). Newton’s Second Law of Motion states that ( ) = × = F ma force mass acceleration . If the mass is measured in kilograms (kg) and acceleration in meters per second squared ( ) m s , 2 then the force will be measured in newtons (N). [ ] = ⋅ N Note: 1 1 kg m s . 2 5. If = 1 kg 2.205 lb, convert the weight of the Wright brothers’ plane to kilograms. 6. If acceleration due to gravity is = a 9.80 m s , 2 determine the force due to weight on the Wright brothers’plane. 7. What must be true about the lift force of the Wright brothers’ plane for it to get off the ground? 8. The weight of a fully loaded Cessna 172P is 2400 lb. What lift force is required to get this plane off the ground? 9. The maximum gross weight of a Boeing 787 is 560,000 lb. What lift force is required to get this jet off the ground? Chapter Project Modeling Aircraft Motion Four aerodynamic forces act on an airplane in flight: lift, weight, thrust, and drag. While an aircraft is in flight, these four forces continuously battle each other. Weight opposes lift, and drag opposes thrust. See the diagram below. In balanced flight at constant speed, the lift and weight are equal, and the thrust and drag are equal. 1. What will happen to the aircraft if the lift is held constant while the weight is decreased (say, from burning off fuel)? 2. What will happen to the aircraft if the lift is decreased while the weight is held constant? 3. What will happen to the aircraft if the thrust is increased while the drag is held constant? 4. What will happen to the aircraft if the drag is increased while the thrust is held constant? Lift Weight Thrust Drag Credit: kesu87/123RF
RkJQdWJsaXNoZXIy NjM5ODQ=