An astronaut is standing on the surface of a planet that has a mass of 6.42×1023 kg and a radius of 3397 km. The astronaut fires
a 2.6-g bullet straight up into the air with an initial velocity of 406 m/s. What is the greatest height the bullet will reach? The planet has no atmosphere.
The final calculated height is 22.2 km. By converting 3397 km to meters, we achieve 3397000m. Using the gravitational constant, we compute the gravitational acceleration on the planet in accordance with Newton's law of gravitation, where M and R represent the planet's mass and radius, respectively. As the bullet ascends to its peak height, its kinetic energy transitions to potential energy. We account for the bullet mass and its initial velocity of 406 m/s, simplifying both sides of the equation to ultimately express the height reached as 22.2 km.
