Tilt ice Hockey Stick 

A 53 in ice hockey stick rests against a vertical wall.
The bottom of the stick slides away from the wall. How fast does the
distance, y change with respect to the angle, θ,
which is made by the wall and the stick, when θ is
equals 45^{o}?
Assumption:
 The angle made by the wall and the stick is θ.
 The slipped distance is y.

y = 53 sinθ
dy/dx = 53 cosθ


According to the diagram,
sinθ = y/53
Thus
y = 53 sinθ
Derivative y with respect to θ
dy/dθ = d(53
sinθ)/dθ
=53
cosθ
When θ = 45^{o},
dy/dθ = 53
cosθ = 37.5 in/rad
The derivative of y = 53 sinθ is
dy/dθ = 53 cosθ when θ is
in the range of (0, π/2). Since y is differentiable,
it is continuous, this is shown in the plot of y = 53 sinθ. 