Variation problem

Question

A plane traveling 140 mph with wing area of 195 square feet has a lift of 12,500 pounds. What is the lift if the plane is traveling at 168 mph?

Answer 1

For the same area, lift is proportional to the square of the velocity.

 

Set up a simple proportion:

 

L₁ → v₁²

 

L₂ → v₂²

 

L₂ / L₁ = = v₂² / v₁² = (v₂ / v₁)²

 

L₁ = 12,500 pounds

 

v₁ = 140 mph

 

v₂ = 168 mph

 

L₂ = L₁ (v₂ / v₁)² = (12,500 pounds) [(168 mph) / (140 mph)]²

 

L₂ = 18,000 pounds