Answer:
Step-by-step explanation:
The triangle that was formed has radius 2:
hypotenuse = 2
adjacent = x = 2*cosθ
opposite = y = 2*sinθ
from the first picture on the left, we see that the rod has length of 4.
We then use pythagoras theorem with respect to the triangle formed with the rod, i.e, the opposite leg, and the length of the remaining side (say, L), we have:
2²sin²θ +L² = 4²
On rearranging and making L subject of formula, we have
L = √(16 - 4sin²θ)
or
L = 2√(4 - sin²θ)
Also, the distance of point B is from the center of the circle, and it is:
2cosθ + 2√(4 - sin²θ)
We know that
3.5 revolutions per second means 3.5(2π) per second.
or
7π radians per second
So we try to write the angle formed as:
θ = 7π*t
where t is the time in seconds.
(a)
2cos(7πt) + 2√(4 - sin²(7πt))
at t = 1/21 we substitute for t, and then
2cos(π/3) + 2√(4 - sin²(π/3))
= 1 + √13 or approximately 4.6
(b)
(c)
B = 2cos(7πt) + 2√(4 - sin²(7πt))
dB/dt = - 14πsin(7πt) - { 14π*cos(7πt)sin(7πt)/√(4 - sin²(7πt)) }
