In the last century, the United States rose from the status of second-tier power to being the world's sole superpower. Some worry that the U.S. will be eclipsed in this century by China, but that is not the problem.
There is never just one possible outcome. Instead, there are always a range of possibilities, particularly regarding political change in China. Aside from the political uncertainties, China's size and high rate of economic growth will almost certainly increase its strength in relation to the U.S. But even when China becomes the world's largest economy, it will lag decades behind the U.S. in per-capita income, which is a better measure of an economy's sophistication. Moreover, given our energy resources, the U.S. economy will be less vulnerable than the Chinese economy to external shocks.
Growth will bring China closer to the U.S. in power resources, but as Singapore's former Prime Minister Lee Kwan Yew has noted, that does not necessarily mean that China will surpass the U.S. as the world's most powerful country. Even if China suffers no major domestic political setbacks, projections based on growth in gross domestic product alone ignore U.S. military and "soft power" advantages as well as China's geopolitical disadvantages in the Asian balance of power.