Answer:
The equation that models how far from the tip of the saw is from the wood in terms of time is x(t) = 10×cos(2×π×t) + 17
Step-by-step explanation:
The given parameters are;
Length of the saw blade = 40 cm
Thickness of the wood across = 8 cm
Length of blade between wood saw handle with hand extended = 5 cm
Length of the tip from the wood at the above time = 40 - 8 - 5 = 27 cm
Length of blade between wood saw handle with saw pulled inwards = 25 cm
Length of the tip from the wood at the above time = 40 - 8 - 25 = 7 cm
Time for one complete cycle = 1 second
We note that the basic equation for oscillatory motion is of the form;
x(t) = A·cos(ωt) + d
Where:
A = Amplitude of the motion = (27 - 7)/2 = 10 cm
ω = Angular frequency = 2·π/T
ωt = Motion's phase
t = Time of the motion
d = The middle location = 27 - 10 = 17 cm
T = The time to complete a cycle = 1 s
Therefore;
ω = 2·π
Given that he stars with his arm extended out, we have;
27 = 10×cos(2×π×0) + 17
Therefore, the equation that models how far from the tip of the saw is from the wood in terms of time is x(t) = 10×cos(2×π×t) + 17.
