Shortly after landing, the jet activates its reverse thrusters to slow the plane

Question

Shortly after landing, the jet activates its reverse thrusters to slow the plane clown from 60 m/s to 15 m/s over a distance of 450 m with a constant deceleration. To clarify, the thruster force is directed to the right while the plane velocity is to the left. The mass of the plane is 120.000 kg. and the mass center is located at G. Ignoring effects of aerodynamic drag and friction in the wheels compared to the thrusters, calculate the normal reaction force under the front wheel A at the end of the interval.

Explanation / Answer

Applying vf^2 - vi^2 = 2ad

15^2 - 60^2 = 2(a)(450)

a = -3.75 m/s^2

T = ma = 120,000 x 3.75 = 450000 N

now balancing net moment about point B,

(1.5 x 450000) - (3 x 120000 x 9.8) + (12 x Na) = 0

Na = 237750 N

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