Carbon-14 has a half life of 5730 years, meaning that 5730 years after an organism dies, half of its carbon-14 atoms have decayed to nitrogen atoms. Because of the short length of the carbon-14 half-life, carbon dating is only accurate for items that are thousands to tens of thousands of years old.

Why cant you use carbon-14 to determine the age of a fossil that is older than 60000 years old?

Its has a half-life of about 5,730 years. The short half-life of carbon-14 means its cannot be used to date extremely old fossils. Levels of carbon-14 become difficult to measure and compare after about 50,000 years (between 8 and 9 half lives; where 1% of the original carbon-14 remains undecayed).

Why would carbon-14 dating not be very useful for determining the age of an early hominid fossil?

Every 5,730 years, the radioactivity of carbon-14 decays by half. That half-life is critical to radiocarbon dating. Since carbon-12 doesnt decay, its a good benchmark against which to measure carbon-14s inevitable demise. The less radioactivity a carbon-14 isotope emits, the older it is.