(IGCSE, Jan 2013, q8 adapted) The astronaut David Scott dropped a hammer and a feather from rest, at the same time and from the same height on the moon. The hammer and the feather landed at the same time. Why?

Central to this question is an understanding of the difference between an accelerating object and an object travelling at terminal velocity. Firstly, the experiment is carried out on the moon, which means we can assume there is no air resistance force, or drag, acting on the two objects. As weight is the only force acting on the objects, and it is a constant force, by Newton's second law of motion, F=ma, we know that the objects will experience a constant acceleration towards the centre of the moon. The forces acting on the hammer and the feather respectively are m_hammer x g_moon and m_feather x g_moon. Using this information, we can construct particular versions of Newton's second law for each object: Hammer: m_hammer x g_moon = m_hammer x a_hammer (1) Feather: m_feather x g_moon = m_feather x a_feather    (2) We can see that in both (1) and (2), the masses cancel from both sides of the equation. This means that g_moon=a_hammer=a_feather. This leads us to the surprising conclusion that the masses of the hammer and the feather don’t matter in determining how quickly they accelerate towards the centre of the moon, and they will land at the same time. Given the time, I’d like to include a historical anecdote about Galileo’s similar (thought) experiment dropping a rock and a feather from the tower of Pisa, and the way he explained the fact that they would hit the ground in the same time without invoking Newton’s second law, which had not yet been formulated.