Why does an object appear to be moving faster as it moves away from the axis of rotation

I suppose that this is a problem of rotation with constant angular velocity.

This can be answered with arcs.

Suppose that we have a circle of radius R, and an angle A (A expressed in radians)

The length of that arc will be:

L = R*A

Now, a rotating object that rotates at a constant angular velocity, in a time t moves an angle A.

so if this object is moving in a circle of radius R, in the time t the distance traveled is the same that we found above.

L = R*A

Now, if the object moves away from the axis of rotation, we have that the radius of the circle R increases, then also does the value of L (the distance traveled in the time t)

Then, when the object moves away from the axis of rotation, in the same time t, the distance traveled will be higher, which means tath the tangential velocty increased (regardless the fact that the angular velocity is constant)

he kicked it 10 feet straight up into the air? i think this works.