In cats, the long hair trait is dominant and the short hair trait is recessive. What is the chance of a homozygous short-haired offspring if a heterozygous long-haired male mate with a short-haired?

the chance of a homozygous short-haired offspring if a heterozygous long-haired male mate with a short-haired is 50%

Explanation:

The best way to see this is to simply draw a punnett square. As you've said, let's call  

S

the dominant trait (short hair) and  

s

the recessive trait (long hair):

As shown in the image i uploaded:

As you can see, out of the 4 possible outcomes, 2 will result in short hair, and 2 in long. So, you'd have a  chance of getting a short haired cat.

✿   this landform has a high elevation and a high relief

✿   this landform is a mountain