A man of mass 78.5 kg walks down the aisle of an airplane at a speed of 1.40 m/s in the forward direction while the plane moves at a speed of 320 m/s relative to the earth.

(a) Find the man's kinetic energy relative to the plane.
(b) Find the man's kinetic energy relative to the earth.

To solve this problem, we need to calculate the kinetic energy of the man relative to both the plane and the Earth.

(a) To find the man's kinetic energy relative to the plane, we can use the formula for kinetic energy:

Kinetic energy (KE) = 0.5 * mass * velocity^2

Given:
- Mass of the man (m) = 78.5 kg
- Velocity of the man relative to the plane (v_relative) = 1.40 m/s

Using the formula, we have:

KE_relative to plane = 0.5 * m * v_relative^2

Plugging in the values, we get:

KE_relative to plane = 0.5 * 78.5 kg * (1.40 m/s)^2

Calculating this expression will give us the man's kinetic energy relative to the plane.

(b) To find the man's kinetic energy relative to the Earth, we need to consider that the plane is moving at a speed of 320 m/s relative to the Earth.

The velocity of the man relative to the Earth (v_earth) will be the combination of his velocity relative to the plane and the velocity of the plane relative to the Earth:

v_earth = v_man_relative_to_plane + v_plane_relative_to_earth

Given:
- Velocity of the plane relative to the Earth (v_plane_relative_to_earth) = 320 m/s

Using the given values, we find:

v_earth = 1.40 m/s + 320 m/s

Now that we have the man's velocity relative to the Earth, we can plug it into the formula for kinetic energy:

KE_relative to Earth = 0.5 * m * v_earth^2

Plugging in the values, we can calculate the man's kinetic energy relative to the Earth.

Remember to convert the units to the appropriate SI unit (joules) for kinetic energy calculations.