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## Homework Statement

A friend of mine and me were walking through the city when he looked up at a tall building, let's say 25 metres, and said "I wonder how long it'd take to hit the ground if you jumped off". I was thinking about it and realized I didn't even know what the appropriate technique(s) are to solve such a problem.

So: where should I begin if I have an object and a height, (on Earth), and I want to know roughly how long that object would take to hit the ground when dropped from that height?

## The Attempt at a Solution

I first thought about the old speed = distance/time formula. Obviously I want not speed but time as the subject so I pondered time = distance/speed. But of course the speed would be changing all the time due to acceleration from gravity. This made me think I should be using calculus. But I don't really know any apart from bare basic differentiation.

So I suppose I could figure out something like, 'the object has fallen 9.8m after 1 sec, then 9.8 + 9.8(2)m after 2 secs' etc. but if that's even correct, surely there's a better way - what do I do if I end up with a distance greater than the height of the building?

So then I thought I needed to integrate something but I have only done indefinite integrals which I think gives you a function from which you differentiate to get that which you just integrated. But I have no clue either what that function should look like, or what function I should be integrating, or if my friend's question can even be answered with basic calculus.

Would I have to compute something like, time = distance/9.8ms

^{-2}?

Thankyou.