Find the x and y coordinates of an object's position at t = `t1 seconds and at t = `t2 seconds, given that at t = 0 seconds its angular position is 0 radians, and that it moves at constant angular velocity of .714 rad/sec around a circle of radius 5.6 meters, making a revolution every 8.8 seconds.
The object has angular velocity `omega = .714 radians/second. Therefore, after 2.5 seconds, starting at 0 radians when t = 0, the angular position will be
`theta1 = ( .714 radians/second)( 2.5 seconds) = 1.785 radians.
On a circle of radius 5.6 meters, the x and y coordinates will therefore be
x1 = 5.6 meters * cos( 1.785 radians) = -1.191 meters
and
y1 = 5.6 meters * sin( 1.785 radians) = 5.472 meters.
After 13.58 seconds, the angular position will be
`theta2 = .714 radians/second( 13.58 seconds) = 9.696119 radians.
On a circle of radius 5.6 meters, the x and y coordinates will therefore be
x2 = 5.6 meters * cos( 9.696119 radians) = -5.396 meters
and
"y2 = 5.6 meters * sin( 9.696119 radians) = -1.501 meters.