Question

What is the initial acceleration of the plane? What is the acceleration of the plane at the point of take-off?

During take-off a jet airplane of mass 10000kg can produce a maximum thrust of 40kN, At the point of take-off, the plane experiences a drag force of 20kN.
a)Calculate the initial acceleration of the plane.
b)Calculate the acceleration of the plane at the point of take-off.

Answer 1

Initially, the acceleration is `4 m/s^2`. At takeoff, it is `2 m/s^2`.

Explanation:

In both cases, we need to evaluate the net force acting on the plane. This net force will, according to Newton's second law, be equal to `ma`, and because we know the mass, the acceleration `a` can be found.

Initially, the only force is the thrust of the engines, so

`F_"net" = ma = 40 000 N`

`a = (40 000)/ (10 000) = 4 m/s^2`

At the point of takeoff, there is also a drag force of 20 000 N that opposes the thrust, leaving a net force of `40 000 - 20 000 = 20 000 N`

`F_"net" = ma = 20 000 N`

`a = (20 000)/ (10 000) = 2 m/s^2`