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‘Climb’ RAs and Performance Limitations
From SKYbrary Wiki
If an ACAS RA occurs when the aircraft is at the maximum altitude for its current weight, the pilots should not assume that they cannot comply with a climb RA because of that. In these cases it is acceptable and assumed that speed will be traded for height. Some aircraft types have built-in inhibits which will preclude Climb RAs at maximum altitudes.
Whether or not inhibits apply, it is still possible in some cases for an RA to exceed the capabilities of the aircraft. If a Stall Warning is generated, it takes precedence over an ACAS RA. ACAS II will not make any aural TA or RA annunciations when a Stall Warning has been activated and it will automatically be placed into TA-only mode (the functionalities of TCAS traffic displayed will not be lost).
Pilots must respond to all RAs a timely manner, applying the vertical rate required by the RA as accurately as possible in the circumstances and must never manoeuvre opposite to a RA.