Which of the following implies a clearance is granted for takeoff?

The phrase "cleared for takeoff" is the standard terminology used in air traffic control to indicate that an aircraft is authorized to take off from the runway. This phrase conveys to the pilot that it is safe to begin takeoff procedures, ensuring that all necessary conditions and safety checks have been satisfied.

When air traffic control issues this specific phrase, it signifies that the aircraft has been given the green light to proceed, taking into account traffic conditions, runway availability, and any other relevant factors that would ensure a safe departure. This clarity in communication is essential for maintaining safety and efficiency in the busy environment of air traffic operations.

Other options, while related to flight operations, do not specifically indicate permission to take off. For example, a launch clearance or departure authorization might pertain to pre-flight checklists or ensuring an aircraft is set for takeoff, but they do not explicitly convey the same level of authorization as "cleared for takeoff." Similarly, runway entry clearance typically means that an aircraft is authorized to enter the runway but does not necessarily imply that it can take off at that moment.