Question

In order for planes to take off from an aircraft carrier deck, they need an initial speed boost. This initial speed is provided by the aircraft carrier in the form of a catapult system (using either steam or electromagnetic force). We want to take off an F-22 from an aircraft carrier. The F-22 has a mass of 21430 kg and the aircraft catapult pushes the airplane across its 98 m long flight deck with a constant force of 415000 N. Assume the flight deck is level. a) What is the velocity of the F-22 as it leaves the flight deck? b) If the aircraft carrier flight deck is 21 m above the ocean surface, then how much time does the F-22 have to begin flying once it leaves the flight deck? c) How far away from the aircraft carrier does the F-22 travel in the time calculated in part b) (assume the aircraft carrier remains stationary and the plane does not start flying)?

Answer 1

a) V = 61.608 m/s

b) t = 2.05 s

c) d = 126.26 m

Step-by-step explanation:

In order to calculate speed, we will need the acceleration. Which is given by:

`a = (F)/(m) = 19.365m/s^2`

Now, the speed after traveling 98m with this acceleration:

`Vf^2 = Vo^2+2*a*d`

`Vf = √(2*a*d)  = 61.608m/s`

For the amount of time from part (b):

`Yf = Yo + Vy * t - (g*t^2)/(2) = 21 + 0 - (10*t^2)/(2)  = 0` Solving for t:

t = 2.05s

Now, with this time, we calculate the distance:

d = V*t = 126.26m