m2 differentiation (1)

(a) Distance between the wall and B
= √(130^2 - 50^2)
= 120 cm
Time taken = 120/30 = 4 s
The required speed of B
= 120 / 4
= 30 cm/s

(b) Let x cm be the distance between A and the ground, then let the distance between B and the wall be y = √(130^2 - x^2) cm, i.e. √(16900 - x^2) cm
tan θ = x/y
y tan θ = x
Differentiate both side w.r.t. t,
y sec^2 θ * dθ/dt + tan θ * dy/dt = dx/dt
√(16900 - x^2) sec^2 θ * dθ/dt + tan θ * dy/dt = dx/dt
(120)(130/120)^2 * dθ/dt + (50/120)(30) = -30
dθ/dt = -0.302 rad, cor. to 3 sig. fig.
Hence θ is decreasing at a rate of 0.302 rad.