Final answer:
To determine the maximum height reached by a body projected with half the escape velocity, we apply the conservation of energy principle. The initial kinetic energy is converted into gravitational potential energy until the body's velocity becomes zero at the maximum height.
Step-by-step explanation:
The question asks about the maximum height reached by a body projected vertically from the surface of the Earth with a velocity equal to half of the escape velocity. The escape velocity is the speed needed to break free from a planet's gravitational pull without further propulsion. As the body is projected with half this velocity, it will climb until its kinetic energy is converted into gravitational potential energy, at which point the velocity becomes zero, and the body starts falling back to Earth.
In this scenario, conservation of energy principles would be applied. Initially, the body has kinetic energy due to its speed and gravitational potential energy due to its height above Earth's surface. As the body ascends, its speed decreases and hence its kinetic energy decreases, while its gravitational potential energy increases. When the body reaches its highest point, all its initial kinetic energy would have been converted into potential energy.
By setting the initial kinetic energy (associated with half the escape velocity) equal to the gravitational potential energy at the maximum height, we could solve for the maximum height achieved.