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.

22.2 km

Explanation:

3397 km = 3397000m

Let gravitational constant . We can calculate the (constant) gravitational acceleration on this planet using Newton's gravitational law

where M and R are the mass and radius of the plannet, respectively

When the bullet is travelling to its highest point, its kinetic energy is converted to potential energy:

where m is the bullet mass and h is the vertical distance traveled, v = 406 m/s is the bullet velocity at the firing point

We can divide both sides by m

or 22.2 km

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