Question

When a pilot banks an aircraft moving at a speed v, in metres per second, at an angle 𝜃,
the radius of the turn that results is given by the formula
2
tan
2
v
r
g


 
= −    
, where g is
the acceleration due to gravity, or 9.8 m/s2
. Use an appropriate equivalent
trigonometric expression to prove that this formula can be simplified to
2
tan
v
r
g 
= .