# Gravitation problem about throwing an object upward

## Homework Statement

Standing on the surface of a small spherical moon whose radius is 6.00*104 m and whose mass is 7.50*1018 kg, an astronaut throws a rock of mass 2.05 kg straight upward with an initial speed 38.5 m/s. (This moon is too small to have an atmosphere.) What maximum height above the surface of the moon will the rock reach?

g=GM/r2

## The Attempt at a Solution

I calculated g, then used the kinematic equation Δy = (vf2 - vi2) / 2a, but it didn't work! Did I use the wrong equations?

gneill
Mentor

## Homework Statement

Standing on the surface of a small spherical moon whose radius is 6.00*104 m and whose mass is 7.50*1018 kg, an astronaut throws a rock of mass 2.05 kg straight upward with an initial speed 38.5 m/s. (This moon is too small to have an atmosphere.) What maximum height above the surface of the moon will the rock reach?

g=GM/r2

## The Attempt at a Solution

I calculated g, then used the kinematic equation Δy = (vf2 - vi2) / 2a, but it didn't work! Did I use the wrong equations?

Yup. The kinematic equations involving g that we use near the surface of the Earth are valid when g remains essentially constant over the trajectory of the projectile. This holds because the relative change in the radial distance from the center of the Earth is negligible, and g = G*M/r.

For your moon, the radius is relatively small and the upward launch speed will take the projectile a distance that is not negligible with respect to that radius.

You would be better to use a conservation of energy approach, using the appropriate expression for the gravitational potential energy as a function of radial distance.