Question

An air jet is flying with a constant speed at an angle of 30° above the horizontal as indicated in the figure below. The weight ⃗ of jet has magnitude W = 86 500 N and its engine provide a forward thrust ⃗ of magnitude T = 103 000 N. In addition, the lift force ⃗ (directed perpendicular to the wings) and the force ⃗ of air resistance (directed opposite to the motion) act on the jet. Determine the magnitude of ⃗ and ⃗ . (5)

Answer 1

To determine the magnitude of the lift force ⃗ and the force of air resistance ⃗ acting on the jet, we need to resolve the weight ⃗ and the forward thrust ⃗ into their horizontal and vertical components.

The weight ⃗ can be resolved into two components:

- the vertical component, Wsin(30°), acting downward

- the horizontal component, Wcos(30°), acting to the left

The forward thrust ⃗ can also be resolved into two components:

- the vertical component, Tsin(30°), acting upward

- the horizontal component, Tcos(30°), acting to the right

Since the jet is flying at a constant speed, the lift force ⃗ must be equal in magnitude to the weight component acting downward, Wsin(30°). Therefore, the magnitude of ⃗ is 86,500 Nsin(30°) = 43,250 N.

The force of air resistance ⃗ is equal in magnitude to the horizontal component of the weight, Wcos(30°), minus the horizontal component of the forward thrust, Tcos(30°). Therefore, the magnitude of ⃗ is (86,500 Ncos(30°)) - (103,000 Ncos(30°)) = -8,715 N, where the negative sign indicates that the force of air resistance is acting in the opposite direction to the motion of the jet.

Therefore, the magnitude of the lift force ⃗ is 43,250 N and the magnitude of the force of air resistance ⃗ is 8,715 N.