Acceleration = (change in speed) / (time for the change)
Acceleration = (990 m/s) / (35 sec) = 28.29 m/s²
Force = (mass) x (acceleration)
Force = (250,000 kg) x (28.29 m/s²) = 7.07 million Newtons
about 1.59 million pounds .
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There you have the Physics and the Math.
Does any of this resemble the real world ?
No. The question is completely bogus.
-- Take-off speed can't be 990 m/s.
That would be about 2,200 mph, almost 3 times the speed of sound.
-- The take-off run can't accelerate at 28.3 m/s² .
That would be almost 3 G's. If it didn't rip the wings off of the 747,
it would surely guarantee early use of most of the passengers' barf bags.
-- The Saturn V first-stage booster that sent Apollo to the moon
had a thrust of 7.5 million pounds. I'm pretty sure that was more
than 4.7 Boeing 747's.
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Ah hah ! I've just been handed a bulletin, or as they say nowadays,
there is breaking news !
I see that the take-off speed has been revised downward to 90 m/s.
That's right at 200 mph which seems reasonable to me, so let's go
back and do the whole thing again:
Acceleration = (change in speed) / (time for the change)
Acceleration = (90 m/s) / (35 sec) = 2.57 m/s² (about 0.26 G)
Force = (mass) x (acceleration)
Force = (250,000 kg) x (2.57 m/s²) = 643 thousand Newtons
about 144 thousand pounds.
about 1.9% of a Saturn V booster.
I like that a lot better.