Astronauts Jump So High on Moon: Weight and Atmosphere Matter

[allstar1]

Astronauts on the Moon can jump so high because

1) they weigh less there than they do on Earth.
2) their mass is less there than it is on Earth
3) there is no atmosphere on the Moon

I believe the correct answer is 1, because they weigh less.

Choice 2 has got to be wrong since mass is always the same on Earth or moon. But I'm not so particularly sure about 3, there is no atmosphere on the moon but i don't know if that has any effect.

 

[Tzar]

The fact that there is no atmosphere does have an effect as it means there is no air friction to slow you down. However, the fact that the moon has a much smaller mass and thus you have smaller weight is far more significant. I would also say 1

 

[andrevdh]

The weigh of an object on a planet comes from the attraction of the object by the planet. According to Newton's universal gravitational law it is given by
$$F=G\frac{m_p m}{r^2}$$
where m is the mass of object (astronaut) and
$$m_p$$
is the mass of the planet. If you were to compare the ratios
$$\frac{m_p}{r^2}$$
for the Earth and the moon you will find that the force (weight) of the object (astronaut) is approximately seven times less on the moon than on the earth. Now for the jumping part - when you jump you launch yourself off the surface by extending your legs - your leg muscles propel you upwards until your feet leave the ground. That is you propel yourself upwards at an increasing speed until you reach some final speed when your legs are extended. After that it is vertical projectile motion with a certain initial upwards velocity. Now due to your reduced weight on the moon you will be able to reach a higher launching speed plus due to the lower gravitational acceleration on the moon (also seven times less than that on earth) you will reach a higher height, even if you did launch yourself upwards at the same speed as on the earth!