Question

if a clown lets go of a rope that has an object attached to it traveling in a circular motion, what will happen to the object

Answer 1

Newtons first law: it continues in a straight path, or in the direction it was moving at the time of release. That path is tangent to the circle it was moving in.

Answer 2

It will follow the trajectory of a projectile that has an initial velocity equal to the velocity it had when it was released. The trajectory will be a parabola, and it will eventually hit the ground.

Answer 3

I agree with Dr WLS, I ignored gravity, but gravity will force it in a parabolic path downward.