Antiderivatives launch

Question

A fighter aircraft is launched from the deck of a nimitz-class carrier with the help of a steam catapult. If the aircraft is to attain a takeoff speed of at least 240 ft/sec after traveling 800ft along the flight deck, find the minimum acceleration ti must be subjected to, assuming it is constant

Answer 1

You don't need calculus for this.

v = velocity - given

a = acceleration - it's what we want

s = distance - given

t = time, but we have two equations, so we can eliminate it.

v = a t, or t = v / a

s = 1/2 a t^2

so

s = 1/2 a (v / a)^2

or

s = 1/2 (v^2 / a)

or

a = 1/2 (v^2 / s)

or

a = 1/2 (240^2 / 800) = 36 feet / sec^2

That's just a little more than 1 G.  Seems low.