1 A formula for calculating the lift force acting on the wings of an aircraft moving through the air is of the form $$F = k v ^ { \alpha } A ^ { \beta } \rho ^ { \gamma }$$ where \(F\) is the lift force in newtons,
\(k\) is a dimensionless constant,
\(v\) is the air velocity in \(\mathrm { m } \mathrm { s } ^ { - 1 }\),
\(A\) is the surface area of the aircraft's wings in \(\mathrm { m } ^ { 2 }\), and
\(\rho\) is the density of the air in \(\mathrm { kg } \mathrm { m } ^ { - 3 }\).
By using dimensional analysis, find the values of the constants \(\alpha , \beta\) and \(\gamma\).
[0pt] [6 marks]