6.4 Exercise 57

In a later chapter, you will find that the weight of a particle varies with altitude such that $w = \frac{m g r_{0} ^{2}}{r^{2}}$ where $r_{0} ^{}$ is the radius of Earth and r is the distance from Earth’s center. If the particle is fired vertically with velocity $v_{0} ^{}$ from Earth’s surface, determine its velocity as a function of position r. (Hint: use $a^{} d r = v^{} d v ,$ the rearrangement mentioned in the text.)