HP-15C The time an object takes to fall to the ground

[Gamo]

According to the User's Manual Page 14 example of the basic programing about
the time an object takes to fall to the ground.

I try to find the exact second from the distance from it.

Second Height (Meter)
1 4.9
2 19.6
3 44.1
4 78.4

Percent difference between 4.9 to 19.6 is 300% when add 78.4 + 300% = 313.6
313.6 meter using the programed formula equal to 8 second

8 313.6
16 1254
32 5016
64 20064
128 80256

the number in seconds is 8, 16, 32, 64, 128 look like a computer bits numbers.
Just curious and share the though.....

[Dieter]

(12-11-2016 11:49 AM)Gamo Wrote:  According to the User's Manual Page 14 example of the basic programing about
the time an object takes to fall to the ground.

I try to find the exact second from the distance from it.

Second Height (Meter)
1 4.9
2 19.6
3 44.1
4 78.4

The formula is heigth [m] = 4,9 x time[s]^2
Where 4,9 is 1/2 of the well known 9,8 m/s here on earth.

(12-11-2016 11:49 AM)Gamo Wrote:  Percent difference between 4.9 to 19.6 is 300% when add 78.4 + 300% = 313.6

19,6 simply is 4x 4,9. And 313,6 is 4x 78,4.

(12-11-2016 11:49 AM)Gamo Wrote:  313.6 meter using the programed formula equal to 8 second

Sure. If the time doubles, the height changes by a factor of 2² = 4. Or +300%, if you prefer.

Or: if the height quadruples (from 78,4 to 313,6 m) this means that the time changes by a factor of 2, e.g. here from 4 to 8 seconds.

(12-11-2016 11:49 AM)Gamo Wrote:  8 313.6
16 1254
32 5016
64 20064
128 80256

the number in seconds is 8, 16, 32, 64, 128 look like a computer bits numbers.
Just curious and share the though.....

I'm not sure what to want to say with the last table, but it's nothing but simple math. ;-)
If you add 300% to the height, i.e. multiply the height by 4, the corresponding time doubles (=sqrt(4)), as do the listed seconds (8, 16, 32, ...).

Dieter

[Vtile]

Actually because of the standard gravity ~9,81 m/s^2 (9,78..9,32 /wiki/) is only approximation, that formulae would give wrong answers depending if you are doing the experiment in equator or in the poles. Also Dieter you forgot one 1/s at your answer, it is not speed, but acceleration.

[Dieter]

(12-12-2016 11:33 AM)Vtile Wrote:  Actually because of the standard gravity ~9,81 m/s^2 (9,78..9,32 /wiki/) is only approximation, that formulae would give wrong answers depending if you are doing the experiment in equator or in the poles.

Mother Nature doesn't work with more than two significant digits. The 15C program uses a rounded value of 4,9 m/s². Which should be OK for most places on earth. ;-)

(12-12-2016 11:33 AM)Vtile Wrote:  Also Dieter you forgot one 1/s at your answer, it is not speed, but acceleration.

Right, there really is a "²" missing.

Dieter

[Gamo]

Math is beautiful !!!
Very helpful comment
Thank You every one.

[Dave Shaffer]

(12-12-2016 07:55 PM)Dieter Wrote:  Mother Nature doesn't work with more than two significant digits. The 15C program uses a rounded value of 4,9 m/s². Which should be OK for most places on earth. ;-)

Not so fast - depends on what you are doing!

Mother Nature may need 12 or 13 significant digits: in our geodesy research, we use very fancy gravimeters (look up in wikipedia) that can measure "g" (the local gravitational acceleration) to parts per trillion! With this precision, you can measure solid earth tides: the ground under your feet cycles up and down twice per day at the tens of centimeters level.

[Vtile]

(12-21-2016 08:38 PM)Dave Shaffer Wrote:  

(12-12-2016 07:55 PM)Dieter Wrote:  Mother Nature doesn't work with more than two significant digits. The 15C program uses a rounded value of 4,9 m/s². Which should be OK for most places on earth. ;-)

Not so fast - depends on what you are doing!

Mother Nature may need 12 or 13 significant digits: in our geodesy research, we use very fancy gravimeters (look up in wikipedia) that can measure "g" (the local gravitational acceleration) to parts per trillion! With this precision, you can measure solid earth tides: the ground under your feet cycles up and down twice per day at the tens of centimeters level.

Well that is what I call a cool bit of information. Yes, mother earth do not work with two significant digits like this air floatation effect (lost in translation, Iirc it had a decent one word name) in very light, but large by volume objects.