Final answer:
The Jamestown colony faced internal conflicts, conflicts with Native tribes, lack of food, and poor health conditions. John Smith helped maintain peace with the Native Powhatan tribe, tobacco cultivation provided a profitable cash crop, and a headright system encouraged immigration and increased the colony's workforce.
Step-by-step explanation:
The Jamestown colony faced several major problems, including internal conflicts among the English settlers, conflicts with the Native Powhatan tribe, lack of food and poor health conditions. These challenges almost led to the complete destruction of the colony during the winter of 1609-1610, also known as 'the starving time.' However, the colony was able to survive and eventually thrive by solving these problems.
John Smith, one of the leaders of Jamestown, played a crucial role in dealing with the Powhatan Indians and maintaining peace. The introduction of tobacco cultivation by John Rolfe provided a profitable cash crop for the colony, which helped to make it economically sustainable. Additionally, the colonists established a headright system to encourage immigration and the establishment of new settlers, which helped to increase the colony's population and workforce.