Four basic forces are in action during flight: weight, lift, thrust, and drag. To fly through the air, an object must overcome its own weight. To do this, it must create an upward force called lift. To generate lift, a forward motion called thrust is needed. The thrust must be great enough to overcome air resistance, which is called drag.
For a commercial jet aircraft, a quick climb is important to maximize efficiency because the performance of an aircraft is enhanced at high altitudes. In addition, it is necessary to clear obstacles such as buildings and mountains and to reduce noise in residential areas. In the diagram, the angle θ is called the climb angle. The velocity of the plane can be represented by a vector v with a vertical component ˆ¥vˆ¥ sin θ (called climb speed) and a horizontal component ˆ¥vˆ¥ cos θ, where ˆ¥vˆ¥ is the speed of the plane.
When taking off, a pilot must decide how much of the thrust to apply to each component. The more the thrust is applied to the horizontal component, the faster the airplane gains speed. The more the thrust is applied to the vertical component, the quicker the airplane climbs.

(a) Complete the table for an airplane that has a speed of ˆ¥vˆ¥ = 100 miles per hour.

(b) Does an airplane's speed equal the sum of the vertical and horizontal components of its velocity? If not, how could you find the speed of an airplane whose velocity components were known?
(c) Use the result of part (b) to find the speed of an airplane with the given velocity components.
(i) ˆ¥vˆ¥ sin θ = 5.235 miles per hour
ˆ¥vˆ¥ cos θ = 149.909 miles per hour
(ii) ˆ¥vˆ¥ sin θ = 10.463 miles per hour
ˆ¥vˆ¥ cos θ = 149.634 miles per hour

Transcribed Image Text:

Lift Thrust Climb angle 0 Velocity Drag Weight 0.5° 1.0° 1.5° 2.0° 2.5° 3.0° ө ||v| sin 0 I 0 v| cos