for the center:
x = 24 cos 45 * t = 17 t
y = 24 sin 45 * t = 17 t
relative to center
initial angle of point from x axis
Ai = 90 degrees (on y axis)
r = 1.5
Xrel = r cos A
Yrel = r sin A
A = 90 + (360*3)t
A = 90 + 1080 t
cos A = cos (90 + 1080t)
= -sin(1080 t) trig identity
sin A = cos(1080 t)
so
Xrel = -1.5 sin (1080 t)
Yrel = 1.5 cos (1080 t)
and sum the x and y components
xpoint = 17 t -1.5 sin (1080 t)
ypoint = 17 t +1.5 cos (1080 t)
you can do conversion to polar coordinates I am sure if needed.
Note my angles are in degrees, not radians
A hockey puck of diameter 3 inches is spinning around its center at a speed of 3 counterclockwise rotations per second. The center of the puck is traveling at a speed of 24 inches per second at an angle of 45 degrees to the positive x-axis.
(a) At time t=0, the center of the puck is at the origin. Where is the center of the puck at time t? (Time t is measured in seconds.)
(b) A point on the outer edge of the puck begins at the point (0,3/2). What is its location at time t?
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