twin engine jet like a 737 may, at the worst case,
The man already stated the words "worst case"above. Assume engine failure and simultaneous fire warning at V1. Aircraft accelerates on one engine to VR. Under
worst case of aircraft being take off climb limited - and that could mean at
worst case as low as 1.6 percent climb gradient or less in a curved take off procedure. With an airspeed of 150 knots, the rate of climb
at worst case would be around 240 feet per minute. Time to reach 400 feet is two minutes and forty seconds.
That's an awful long time before you get down to the nitty gritty of going through the usual SOP of captain/first officer agreement of first agreeing on which engine has failed and is on fire. Then the closing of thrust lever, followed by agreement which start lever is cut-off; followed by mutual agreement of which fire switch to actuate followed by agreement on bottle firing. And all this doesn't start until reaching a `safe` height of above 400 feet.
Of course, the chances of that scenario happening is extremely rare indeed. But there again, the chances of a crew losing control and stalling an Air France A330 at 38,000 ft while the captain just happened to be on rest down the back is also very rare indeed. But it happened.