First, math is the language of both physics and engineering.
If you can’t do math - well - then you can’t do physics or engineering.
If you can’t do it, you don’t understand it.
It’s just that simple.
The amusing part is that you didn’t have to do one iota of calculus to answer 2 of the 3 questions that I asked you.
I asked:
Generate the velocity vs time equation.
Calculate the terminal velocity
Find the acceleration versus time equation
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The point here is that you really didn’t have to do ANY calculus to demonstrate you knew a bit about these topics.
But you don’t know squat about them.
All you can do is strut around like a buffoon, claiming that you do …
… and then fall flat on your face when asked to prove it.
__
And THIS comment proves that you do NOT have even the simplest, most remedial level of understanding of high school physics.
Look in the mirror. Look into your own eyes.
Say in a firm voice, "You, False Flag, know NOTHING about physics.”
Rinse. Repeat as often as necessary.
At least once before each time you’re inclined to post here on the subject.
If you can’t do math - well - then you can’t do physics or engineering.
If you can’t do it, you don’t understand it.
It’s just that simple.
The amusing part is that you didn’t have to do one iota of calculus to answer 2 of the 3 questions that I asked you.
I asked:
OK, here's a simple opportunity for you to prove it.
NIST provides … an empirical equation for the drop of the roofline of WTC7 vs. time.
[Eqn. 1] z(t) = 379.62 (1 - e(-0.18562 t)3.5126)
where z = the drop of the roofline from its original position.
You can see from the data that this curve fits the data far better than the velocity vs. time graph, shown in figure 12-77.
Use Eqn 1, above to generate: [Note: I’ve reversed the order of the 2nd & 3rd questions. -tk]
the velocity vs. time equation
calculate the terminal velocity.
the acceleration vs. time equation
Generate the velocity vs time equation.
- 1. If you had opened your eyes, or knew what you were looking at, you would have realized that the answer to this question was staring you in the face. Do you see the equation in the top left corner of the velocity vs time graph? You could have copied & pasted it.
No math required.
But you don’t know how to read these graphs well enough to understand these simple principles.
v(t) = 247.5 (0.1856 t)2.5126 e(-(0.1856 t)3.5126) - 2. Or, you could have simply said, “you need to take the derivative of z(t) with respect to t”. Or simply, v(t) = d (z(t))/dt. “… but the equation is too complicated for me to solve.” That would have shown you actually understood what is going on.
- 3. Finding the derivative of the z(t) equation is actually pretty simple … if you remember remedial calculus. (i.e., derivatives of exponentials , and the Chain Rule: d(eg(t)) / dt = (d(g(t))/dt) eg(t)) and the simple version of this when g(t) = k => d(ek t) / dt = kek t In this case g(t) = (-0.18562 t)3.5126 then d g(t)/dt = (-0.18562) (3.5126) (-.18562 t)2.5126 = 0.6520 (.18562 t)2.5126 and v(t) = 247.5 (0.1856 t)2.5126 e-(0.1856 t)3.5126[/sup] Whaddaya know. It matches 1 above.
- 4. Or, you can use the tools available today.
I prefer Mathematica.
Define: z[t_] = 379.62 (1 - E^(-(0.18562 t)^3.5126));
Let MMA find the 1st derivative: v[t_] = z'[t] which returns:
v[t] = 3.59707 E(-0.00269756 t3.5126) t2.5126
Calculate the terminal velocity
- First, you should realize that the terminal velocity happens when the acceleration goes to zero. In other words, the maximum of the velocity vs. time graph. If you had merely said this, you would have shown some understanding. Now you should be able to read it straight off of the velocity vs. time graph, and show it is ~ 92 ft/sec.
- Alternatively, you could have stated that the terminal velocity is the slope of the displacement vs. time graph, once the slope has reached it steepest value. You could have stuck a ruler up against the side of the first graph’s curve, between the 4.2 & 5.3 second interval, read off two z displacements & two time values and computed the terminal velocity from Vterminal = Δz / Δt If you had done this, then you would have gotten, surprise, about 92 ft/sec.
- Or, you might have noticed that the velocity maxed out right around 5 seconds. You could have plugged 5 in for t in the velocity vs. time equation & calculated the terminal velocity. If you had done this, you would have gotten, surprise): Vterminal ≈ 95 ft/sec.
- Finally, you could have done it the traditional way. a. Calculate the derivative of the velocity vs. time graph. (which is the answer the 3rd question.) b. Set the acceleration equal to zero, and solve for t (time). c. Plug that time value back into the velocity vs. time equation & calculate the terminal velocity.
- Or you could let Mathematica find the local Maximum of the velocity function:
FindMaximum[v[t], t]
which returns: {95.2501, {t -> 4.89724}}
or a terminal velocity of 95.2 ft/sec.
Find the acceleration versus time equation
- You could have said “take the first derivative of v(t) with respect to t” or “take the 2nd derivative of z(t) with respect to t”. That would have shown you knew what you were talking about.
You made no effort to do so, because you’re lazy. - Go back to school & learn how to do it the old fashioned way: by memorizing a boatload of explicit patterns. You’ll have no hope of doing this, either. In addition to being lazy, you’re intellectually sloppy.
- Or do it the easy way: with Mathematica, MathCAD, Maple or other math programs
With Mathematica, define: a[t_] = v’[t] or equivalently a[t_] = z’’[t] which returns:
a[t] = 9.038 E(-0.00269756 t3.5126) t1.5126 - 0.0340839 E(-0.00269756 t3.5126) t5.0252
__
The point here is that you really didn’t have to do ANY calculus to demonstrate you knew a bit about these topics.
But you don’t know squat about them.
All you can do is strut around like a buffoon, claiming that you do …
… and then fall flat on your face when asked to prove it.
__
And THIS comment proves that you do NOT have even the simplest, most remedial level of understanding of high school physics.
Look in the mirror. Look into your own eyes.
Say in a firm voice, "You, False Flag, know NOTHING about physics.”
Rinse. Repeat as often as necessary.
At least once before each time you’re inclined to post here on the subject.
