Supposing the person has insignificant height, we have that the angle of elevation is connected to the height of rocket and distance from spectator by:
tan(θ) = H/D (opposite is height, adjacent is distance)
Taking the derivative of both sides with respect to time:
d/dt (tan(θ(t))) = v/D (where v is the velocity of the firework)
Using chain rule on the left side:
sec2(θ)*(dθ/dt) = v/D
dθ/dt = cos2(θ)*v/D
When the firework is 30 feet above the ground, θ = tan-1(30ft/15ft) = 0.540 rad
dθ/dt = [ 1 / (1 + 1) ]*(11)/15
= (1/2)(1/15)*(11)
= 11/100
= 0.011 radians /s
