Which factor is crucial for determining the altitude a rocket can achieve?

The thrust-to-weight ratio is a critical factor in determining the altitude a rocket can achieve because it directly influences the rocket's ability to overcome gravitational pull and accelerate upward. This ratio compares the thrust produced by the rocket's engines to its weight.

A higher thrust-to-weight ratio means that the rocket has more thrust than its weight, enabling it to ascend rapidly and reach greater altitudes. Conversely, if the weight is too high relative to the thrust, the rocket may not lift off or may struggle to reach significant heights.

In essence, the thrust-to-weight ratio is a key performance metric in rocketry that dictates the rocket's initial acceleration and its ability to ascend through the atmosphere. Other factors, while relevant, do not capture the same direct relationship to altitude achievement as this important ratio does.