Question

A 10,000 kg jet plane must reach a speed of 60 m / s for takeoff. If the jet engine increases its thrust at a rate of 20,000 N / s. Determine the time it takes for the aircraft to reach takeoff speed. Neglect air resistance and other forces.

Answer 1

Given that:

Mass of jet plane, m = 10000 kg

Rate of increase of thrust, dF/dt = 20000 N/s

We know that, F = ma

d (ma)/dt = 20000 N/s

m.da/dt = 20000 N/s

(10000 kg) . da/dt = 20000 N/s

da/dt = 2 m/s³

That is, rate of change of acceleration is 2 m/s³

Let t be the time taken to reach the take of speed.

(da/dt ) . t² = 60 m/s

t² = (60 m/s) / (2 m/s³)

t² = 30 s²

t = sqrt (30)

t = 5.5 s

• That is, time taken to reach the takeoff speed = 5.5 seconds