This WILL sound sketchy and far-fetched, but read every bit of information carefully, and you will hopefully understand, I know overall the reason why the objects fall together at the same rate is because there is no air-resistance, but working with formulas it shows how some things are inter-linked and how the mass is irrelevant due to the cancellation of mass from the basic GCSE Physics formulas of: "Kinetic energy gained = Gravitational potential energy lost." Copied from my facebook thread: " Students taking the Physics-2 Exam in November 2012: The topic of Kinetic-Energy and Gravitational-Potential-Energy: You are required to learn as part of the Syllabus: The ability to work out Speed of a falling object being given the Mass and the Height of the object from where it starts to fall (assuming the object is falling to the ground on Earth (meaning g = 10N/Kg)). The example that follows shows you how to do this: Kinetic Energy Gained = Gravitational Potential Energy lost. mgh = 1/2mv^2 Whereby: m = Mass in Kilograms (Kg) g = Gravitational Field Strength (Earth being 10N/Kg & The Moon being 1.6N/Kg) h = Height of the object (the height of where the object is falling from to the ground) in meters v = Velocity (in meters per second). ======================================================= Example: An apple of mass 140grams has fell from a tree of height 1.7 meters. Calculate the speed as it hits the floor. First off, the speed "as it hits the floor" is the overall speed the apple is traveling at as it is falling, so lets not get confused by that. Find G.P.E lost: G.P.E = mgh = 0.14 x 10 x 1.7 = 2.38J (J = Joules). This must also be the K.E gained. Equate the number of joules of K.E. gained to the K.E. formula with v in: 2.38 = 1/2mv^2 Stick the numbers in: 2.38 = 1/2 x 0.14 x v^2 or 2.38 = 0.07 x v^2 2.38 / 0.07 = v^2 so v^2 = 34 v = √34 = 5.83 m/s ======================================================= This seems all rather complicated no? This is what the revision book has told me to do (which I have added a couple of sentences here just to clarify what is actually going on, as by the "First off" sentence). It has just dawned to me that if you look at the Height of the object, and times it by 20, that is the Velocity squared. Proof below: Look at the formulas, it is basic cancelling and changing the subject: mgh = 1/2mv^2 Divide both by m (which is mass), because what you do to one side, you MUST do to the other, therefore: gh = 1/2v^2 'g' does not change, and neither does the height, however: g = 10N/Kg (ONLY on the Earth, the question WILL state if the object is falling on the Moon, if so, then the question will tell you that). Therefore: 10h = 1/2v^2 Therefore: 20h = v^2 √(20h) = v This means, no matter what the mass of the object is, it could be 5 Kilograms, it could be 9.9 x 10^4 Kilograms, if you have the height of the object, then you times it by 20 and you then square-root that answer, to find the speed of the object as it is falling on Earth. If it states the "Moon" rather than the "Earth" then you follow these steps: gh = 1/2v^2 Replace g with 1.6 (rather than 10, as 'g' on the moon is 1.6N/Kg) 1.6h = 1/2v^2 3.2h = v^2 √(3.2h) = V Times the Height by 3.2 and then square-root the overall answer to get the Velocity in meters per second. No matter the mass, times the height by 20 (for the Earth) or 1.6 (for the Moon) and you then follow the last couple steps, to get the velocity squared. Overall if I said to you: Mass = 7.65635252345 x 10^14 and Height = 500 meters, would you wnt to write down all the calculations of the first way (which is how they expect you to learn it), or would you just times '500' by 10, and then 2 (to make 1/2v^2 into v^2), and then square-root that to find the speed of the falling object? It works regardless, it just saves you having to mess around with the mass, which could, in any case in real life, be a really confusing decimal number. I found this out about 25 minutes ago (so, about 8:10pm). Joshua Brazier. " Now how it is inter-linked to the falling of the Hammer & Feather on the moon: " This is also the reason why two objects with different masses hit the ground of the moon together: If there is no air-resistance on the moon, which there isn't, mass doesn't have a say in the speed of the object, because the resistance isn't there to slow the object down, therefore just like my formula, mass is irrelevant, meaning: You have two objects with different masses, and drop them at the same time on the moon, they WILL hit the ground together. Also: Speed = Distance / Time This means if you have the height of the object which you do, and you follow my steps, or the steps given by the book, you can work out how long it takes for the object to hit the ground. Meaning: Just like with the Hammer & Feather experiment on the moon: If the Astronaut dropped the object from just above waist height, the height would be 83cm (on average), therefore: Speed = 83cm / Time Time = 83cm / speed Therefore: speed = √3.2h √(3.2x0.83) (0.83 Because the height is in Meters, and not Centimeters). Meaning: √(3.2x0.83) = √2.656 = 1.63 meters per second, Therefore: Time (seconds) = 83cm / 1.63 meters per second Therefore: 0.83 meters (because overall we are using meters per second with speed, and you must then convert the centimeters into meters). 0.83 / 1.63 = 0.51 Seconds (rounded to 3.S.F): Meaning: If you dropped a hammer (or any object for that matter) at 83 Centimeters on the moon (waist height for the average person), then it will take 0.51 Seconds to hit the ground. This is what happened when the Hammer and Feather were dropped together by the Astronaut on the moon. The mass of the objects is irrelevant. Overall, 0.51 Seconds is how long it takes for any mass to fall from 83 Centimeters on the moon. " If anyone has anything to prove me wrong, please tell me, and I will agree and say that I was wrong, although, please read the entire two threads first and then tell me, before making any accusations that I am wrong without fully reading my theory and examples. Thank you. Eggman100 / Joshua Brazier.