Answer:
The correct option is;
16 inches
Explanation:
The parameters of the motion given are;
The diameter, D of the bicycle = 16 inches;
The distance the bike moves (forward) after the screw punctures the tire = 56·π inches
We note that the circumference of the bicycle = π·D = π × 16 = 16·π inches
Therefore;
56·π inches/(16·π inches) = 3.5
Showing that the bicycle moves three and half complete turns (revolution) where after each complete turn, the screw starts from the bottom of the tire.
The height, h of the screw in the final half turn is given by the relation;
h = A×cos(Bx - C) + D
A = Amplitude of the motion = Diameter/2 = 16/2 = 8
P = The period of the motion 2·π/B
B·x = The angle described by the motion = Half of one revolution = π = 180°
C = Phase shift = π
D = The midline = Diameter/2 = 8 inches
Therefore;
h = 8×cos(π - π) + 8 = 16 inches
After the bike moves forward another 56·π inches the height of the screw = 16 inches.