A man of mass 83.5 kg walks down the aisle of an airplane at a speed of 1.60 m/s in the forward direction while the plane moves at a speed of 295 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 find the man's kinetic energy, we need to use the formula:
Kinetic energy = 1/2 * mass * velocity^2
(a) To find the man's kinetic energy relative to the plane, we use the relative velocity between the man and the plane. Since the man is walking down the aisle in the forward direction of the plane, the relative velocity is the difference between the man's velocity and the plane's velocity.
Relative velocity = man's velocity - plane's velocity
Given:
Man's mass (m) = 83.5 kg
Man's velocity relative to the plane (v) = 1.60 m/s
Plane's velocity relative to the earth (V) = 295 m/s
Relative velocity = v - V
Now substitute the values into the formula to calculate the man's kinetic energy relative to the plane:
Kinetic energy relative to the plane = 1/2 * mass * (relative velocity)^2
(b) To find the man's kinetic energy relative to the earth, we need to combine the man's velocity relative to the plane and the plane's velocity relative to the earth. The relative velocity between the man and the earth is the sum of these two velocities.
Relative velocity = man's velocity relative to the plane + plane's velocity relative to the earth
Given:
Relative velocity = v + V
Now substitute the values into the formula to calculate the man's kinetic energy relative to the earth:
Kinetic energy relative to the earth = 1/2 * mass * (relative velocity)^2
Note: Make sure to use consistent units for mass and velocity in the calculations.