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An airplane is flying with constant speed of 300 m/s along a horizontal circle with a radius of 15,000 m. if the lift force of the air on the wings is perpendicular to the wings, at what angle relative to the horizontal should the wings be banked?

Answer :

31.5°
31.5°
31.5°
31.5°
31.5°
31.5°
31.5°
31.5°

Angle; θ ≈ 31. 5°

This question involves centripetal motion and angle of elevation.

  • We are told that the lift force of the air on the wings is perpendicular to the wings.

This means, from centripetal motion we can write the force as;

F•sin θ = mv²/r - - - (1)

Where θ is the angle relative to the horizontal if the wings are banked.

r is radius

v is speed

  • Similarly, resolving the force Component along the horizontal x-axis, we will have;

F•cos θ = mg  - - - (eq 2)

  • We are given radius and speed but we don't have force (F) and mass(M). Thus, we can eliminate them by dividing equation 1 by equation 2 to get;

(F•sin θ)/(F•cos θ) = (mv²/r)/mg

tan θ = v²/rg

Plugging in the relevant values L, we have;

tan θ = 300²/(15000 × 9.8)

tan θ = 0.6122

θ = tan^(-1) 0.6122

θ ≈ 31. 5°

Read more at; brainly.com/question/13692301

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