# Homework Help: How to calculate time when falling off a building

1. Jan 15, 2013

### 3.141592

1. The problem statement, all variables and given/known data

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 realised 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?

3. 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.

2. Jan 15, 2013

### rude man

Ignorimng air resistane,
h = (gt^2)/2 & solve for t. g = your 9.81m/sec^2. h in m, t in sec.

3. Jan 15, 2013

### 3.141592

Thankyou very much. Please can you tell me which area of mathematics I would learn about such things i.e. speeds and distances and times of moving things when the speed is not constant. So obviously beyond the basic s = d/t stuff. Would that be in classical mechanics?

4. Jan 15, 2013

### the_godfather

there is a set of equations relating s, u, v, a and t. they are called the kinematic equations. They should be covered in last couple of years of high school/6th form (years 12 & 13)

5. Jan 15, 2013

### 3.141592

Oh cool, thanks! Yeah I am afraid I stopped at year 11.

s, u, v, a and t.

What is u? And is 'a' acceleration?

Thanks.

6. Jan 15, 2013

### rude man

This question is high school algebra or physics.

If acceleration (g) were not constant then you would have to have covered elementary calculus (1st semester college) and probably 1st semester introductory engineering-level college physics. Example: a car puts out constant power. What is the relationship between distance covered s and time t if s(t=0) = 0? This requires both calculus and probably 1st sem. eng level physics also. The calculus should probably include elementary differential equation solution.

(Ans. s = (2/3)(2P/3m)1/2t(3/2) where P = power, m = mass of car. IF I did it right!)

7. Jan 15, 2013

### the_godfather

u = initial speed
s = displacement
v = final speed
t = time
a = acceleration

8. Jan 16, 2013

### 3.141592

Thankyou both.