calculate average acceleration of airplane during arrest

Question

An airplane lands on an aircraft carrier and is brought to the ships velocity of 10.3 m/s by an arresting cable in a distance of 114 meters. The mass of the air plane is 28,000 kg and it's velocity as it snagged the arresting cable was 58m/s 

calculate the average acceleration of this airplane during arrest 

Answer 1

Let us solve this problem in the reference frame where the aircraft carrier is at rest, assuming constant acceleration over a stopping distance x on the surface of the aircraft carrier.

 

We will use the kinematic relationship 

 

a = (v² - v₀²) / (2x) 

 

v₀ = speed of airplane relative to the aircraft carrier at the moment the cable begins to arrest it

 

The plane approaches the carrier at 58 m/s, but the carrier is moving at 10.3 m/s, so the speed of the airplane relative to the carrier is

 

v₀ = 58 m/s - 10.3 m/s = 47.7 m/s

 

(I am assuming 58 m/s is the "ground" speed of the plane, not the speed of the plane relative to the carrier.  If that is not the case, tell me, and I will adjust the solution.)

 

The plane comes to a full stop on the carrier, so relative to the carrier, its final speed is

 

v = 0

 

The stopping distance is 114 m on the surface of the carrier, so

 

x = 114 m

 

Then

 

a =  (0² - 47.7²) / (2*114) m/s² = -9.98 m/s²

 

The acceleration is negative because the airplane is slowing down.  Note it does not depend on the mass of the airplane.