Arocket is continuously firing its engines as t accelerates away from earth. for the first kilometer of its ascent, the mass of fuel ejected is small compared to the mass of the rocket. for this distance, which of the following indicates the changes, if any, in the kinetic energy of the rocket, the gravitational potential energy of the earth-rocket system, and the mechanicel energy of the earth-rocket system?

a. rocket kinetic energy-increasing system gravitational potential energy-increasing system mechanical energy-constant
b. rocket kinetic energy-decreasing. system gravitational potential energy-increasing sysem mechanical energy-constant
c. rocket kinetic energy-increasing system gravitational potential energy-decreasing sysem mechanical energy-decreasing
d. rocket kineic energy-increasing system gravitational potential energy nreasing syste mechanical energy-increasing

c) True.    Rocket Kinetic Energy-Increasing System Gravitational Potential Energy-decreasing Sysem Mechanical Energy-decreasing

Explanation:

Let's write the three equations.

The kinetic energy is

                      K = ½ m v2

As the speed of the rocket increases the kinetic energy must be increased

The potential energy of the rocket system - Earth

                    U = -G m M / r

As the rocket moves away from the earth the power energy must decrease

Mechanical energy

                 Em = K + U

In this case, if we neglect the energy of the exhaust gases, the mechanical energy remains constant.

if we take into account the energy of the gases, the mechanic energy must decrease due to the loss of the energy that takes them

Let's examine the answers

a) False. The power power l decreases

b) False. The kinetic energy increases

c) True. Meets all of the above

d) False The mechanical energy of the system is constant