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Mathematical Puzzles

Fri Dec 18, 2009 7:54 pm  by Callyst

this is just a formula for the height of an object shot straight up into the air. i found it in my math text book. height equals meters per second subtracted by 4.9 seconds squared. the puzzle is why does the formula use 4.9 instead of 9.8 and why are the seconds squared.


H= ms - 4.9ss
Sun Dec 27, 2009 6:22 am  by applescript

the actual formula should be

s=ut + 0.5at^2

where s is the distance travelled (m)
u is the initial velocity (m/s)
a is the acceleration (m/s^2)
t is time (s)
figures in brackets represent the unit.

For your case, a is the acceleration due to gravity and it is in the opposite direction of that of the velocity.

Therefore s= ut + (0.5)(-9.81)t^2
From there you get, s= ut - 4.9t^2

Mon Jan 04, 2010 7:57 pm  by Callyst

the formula i put down was the same except it was set to determine the height in meters. also i'm still working on this problem and i don't understand why t (seconds) is squared. i understand 9.8 becoming 4.9 but why does gravity continue to accelerate against the initial speed.

example: H= 98m/s - 4.9m/s^2

i'd like to use this for an example problem.
Mon Feb 08, 2010 10:58 pm  by freakawill

This explanation requires calculus.

Let's start from acceleration. 9.8m/s^2 is the acceleration due to gravity. So we can write:

Our y right now is a rate of change of velocity so we can write it as

Let's integrate to find the velocity and call it v.
int(dy/dt=9.8,t)=9.8t + c
v=9.8t + c

Our c is any random arbitrary number but for this equation it is the starting velocity. But this is still the rate of change of distance so let's integrate again getting...
y=k + ct + (9.8)(1/2)t^2
y=k +ct + 4.9t^2

Where k is just like c but instead our initial height.

So basically we derived a general formula for an object with a given acceleration. So why are the seconds squared?
It is a rate of a rate. It is quite literally meters per second per second. To convert to meters, you must multiply by seconds twice.
Sat Jan 18, 2014 11:52 pm  by dave08

i know my physics teacher tell us all the formula about that and i know he teach us that formula.
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