Radius of the ride is feet.

Speed of the ride is   feet per second.

Diagram of the situation:

Find a vector orthogonal to the vector .

The component form of can be using its magnitude and directed angle.

.

Substitute and in the above expression.

The component form of can be using its magnitude and directed angle.

.

Observe the graph, directed angle .

Since the direction of the vector is pointing down, then the vertical component will be negative.

Substitute and in .

(b)

If the dot product of the two vectors is zero, then the two vectors are perpendicular.

Consider the components of the position and velocity vectors.

and .

Thus, the and are perpendicular to each other.

Position vector and tangent velocity vector

and are perpendicular to each other.