Final answer:
The tangential and normal components of acceleration can be determined by finding the velocity and acceleration vectors. The tangential component is parallel to the velocity vector, while the normal component is perpendicular to the velocity vector.
Step-by-step explanation:
The tangential and normal components of acceleration can be determined by finding the velocity and acceleration vectors. The velocity vector, v(t), can be obtained by taking the derivative of the position vector, r(t). In this case, v(t) = (-20sin(t), 20cos(t), 30). The acceleration vector, a(t), can be obtained by taking the derivative of the velocity vector. In this case, a(t) = (-20cos(t), -20sin(t), 0).
The tangential component of acceleration, at, is the component of acceleration that is parallel to the velocity vector. To find the tangential component, we can take the dot product of the acceleration vector, a(t), and the unit vector in the direction of the velocity vector, v(t)/|v(t)|. The normal component of acceleration, an, is the component of acceleration that is perpendicular to the velocity vector. To find the normal component, we can subtract the tangential component from the acceleration vector, a(t).
For the given trajectory, the tangential and normal components of acceleration are:
Tangential component of acceleration: (-20cos(t), -20sin(t), 0)
Normal component of acceleration: (0, 0, 0)