A plane designed for vertical takeoff has a mass of 6.4 ✕ 103 kg. Find the net work done by all forces on the plane as it accelerates upward at 8.4 m/s2 through a distance of 30.0 m after starting from rest.

To find the net work done by all forces on the plane, we can use the work-energy theorem, which states that the net work done on an object is equal to the change in its kinetic energy.

The work done by a force can be calculated using the equation:

Work = Force × Distance × Cos(θ)

Where:
- Work is the net work done
- Force is the net force acting on the object
- Distance is the displacement of the object
- θ is the angle between the force vector and the displacement vector

In this case, the net force acting on the plane is equal to its mass multiplied by its acceleration:

Net Force = mass × acceleration

Before we calculate the net work done, we need to calculate the net force acting on the plane.

Given:
- Mass of the plane, m = 6.4 ✕ 10^3 kg
- Acceleration, a = 8.4 m/s²
- Distance, d = 30.0 m

First, calculate the net force:

Net Force = mass × acceleration
= (6.4 ✕ 10^3 kg) × (8.4 m/s²)

Next, calculate the net work done:

Work = Force × Distance × Cos(θ)

Since the plane is accelerating upwards, the angle θ between the force and displacement vectors is 0 degrees, and Cos(0°) = 1. Therefore, the equation reduces to:

Work = Force × Distance

Finally, substitute the values to calculate the net work done:

Work = (net force) × distance
= (net force) × (30.0 m)