The vertical motion of a general aviation airplane subjected to a sharp-edged wind gust is described by the equation

Δw(t) = A_g(1-e^-t/τ) assume A_g = 30

where Δw is in the vertical velocity, is the magnitude of the wind gust, and g A (1-e^-t/τ)  is the time constant of the airplane. Use the Figure Q3 to determine the following:

(a) State the two types of gust inputs that are commonly used for the modelling process.

(b) Estimate the time constant of the airplane system.

(c) The maximum vertical acceleration and the time at which it occurs.

(d) Airplanes with low wing loadings are more responsive to the influence of vertical wind gusts compared with airplanes with high wing loadings. Verify the validity of the statement above with appropriate reasoning.