A rocket is continuously firing its engines as it 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 mechanical energy of the Earth-rocket system?
1. KE Increases, PE Increases, ME Increases
2. KE Increases, PE Increases, ME Constant
3. KE Increases, PE Decreases, ME Decreases
4. KE Decreases, PE Increases, ME Constant

The correct answer is

1. KE Increases, PE Increases, ME Increases

Explanation:

Here, it is essential to define the following concepts.

Kinetic energy is the energy due to motion of an object. The definition of kinetic energy is the energy to accelerate a body from rest to a given velocity. The body retains the kinetic energy as it maintains the attained velocity

KE= 1/2mv^2

From the above definition KE is increasing

Potential energy is the energy stored within a body due to its location in a position or location of higher potential

As an object moves up to higher altitude in a direction opposite to the earth's attractive force, its gravitational potential increases

PE=mgh

From the above definition PE is increasing

Mechanical energy is the sum of potential and kinetic energies that can be used to do work. It is the sum of the potential and kinetic energies stored in the body

ME = PE+KE

Since both PE and KE are increasing then ME is also increasing

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