From the surface of earth, a body is projected upwards with a kinetic energy equal to one-third of the energy required to escape. Calculate the height up to which the body will rise above the surface of earth.

Explanation

To solve the problem, we need to calculate the height to which a body will rise when projected upwards from the surface of the Earth with a kinetic energy that is one-third of the energy required to escape the Earth's gravitational field.

### Step-by-Step Solution:

1. **Understanding Escape Energy**:
The energy required to escape the gravitational field of the Earth is given by the formula:
\[
E_{\text{escape}} = \frac{GMm}{R}
...