Total mechanical energy concept

I was solving a true or false question regarding total mechanical energy and the following was the problem.

It is possible for a moving object to have negative total mechanical energy.

This is my claim.

Total mechanical energy is defined as

$$M=K+U$$

where $K=\frac{1}{2}mv^2$ and $U=mgh$.

No matter which direction the object is moving $K$ must be positive due to the $v^2$. (I am assuming that mass is also never negative.)

Potential energy is also positive because $g=9.8$ and height is a distance, which is also non-negative.

And yet, the problems says that the answer is true, as in the total mechanical energy is allowed to be negative.

What am I not seeing here ?

Answer

As Kyle implies in the comments, mechanical energy is generally defined only up to a constant. Therefore, if you choose your constant as a large, negative number, you could have a total energy that is negative even with a very fast moving particle. Likewise, if you choose your potential energy to equal zero at, say, the top of a cliff, then anything you throw off the cliff will have negative potential energy once it falls below your feet.

This is not strictly a duplicate, but it is probably worthwhile to link to this answer I posted a while back.