Answer to Question #166597 in Physics for Lucy McGuire

Question

When the astronauts left the Moon, they used a spacecraft with a mass of 2150 kg 

Calculate the height reached by the spacecraft at the point where it had a  gravitational potential energy of 86 000 000 J 

The gravitational field strength of the Moon is 1.6 N/kg 

Answer 1

By definition, the gravitational potential enegry is given as follows:

$$W = mgh$$

where $m = 2150kg$ is the mass of the spacecraft, $g = 1.6N/kg$ is the gravitational field strength, and $h$ is the height reached by the spacecraft. SInce $W = 86 000 000 J$, obtain:

$$h = \dfrac{W}{mg}\\ h = \dfrac{86 000 000 J}{2150kg\cdot 1.6N/kg} =25000m = 25km$$

Answer. 25 m or 25 km.