TBR free-fall shortcut

[katezilla2]

Hey guys,

In TBR Chp 1 on free fall bodies they have a shortcut if for future free-fall problems.

It's basically...
Time- 0.25, 0.5, 1...
Approx h- 0.31,1.25,5.0...
Approx Vt...2.5,5,10....

Could you just memorize that table (knowing time is x2, approx height x4) with those numbers and be able to solve all future free-fall problems without doing any math? I am slightly confused or over thinking something simple. I'm looking through random practice problems on the internet and it seems to be working. Can someone explain how this is working??

Thanks!

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[Cambino]

Well, translational motion in the vertical direction will explain the free-fall calculation trick in TBR...
y = 1/2*a*t^2
deltay = 4.9t^2 which is roughly equal to 5t^2.
This represents the distance traveled in the y-direction of an object in free-fall starting from rest.
Its speed of impact in the y-direction when falling from rest is given by v=9.8t which is roughly 10t.
v = v0 + at

So, if an object is in free-fall starting from rest for 1.5 seconds, it traveled ~(1.5^2)*5 = 11.25 meters in the y-direction, with a velocity of 10*1.5 = 15 m/s toward the ground.

Am I understanding your question correctly?

 

[BerkReviewTeach]

Exactly Cambino. It's simplifying those two equations and then building an arsenal of whole number values to use for approximations in the future.

The BR philosophy is that if you are doing tons of problems in practice, you might as well build a summary sheet that can be used to quickly answer free fall (or horizontal cliff launch or vertical launch) questions.

How high will a projectile launched vertically at 28.2 m/s reach? The shortcut is that it will travel up for 2.82 seconds and that is almost 3 seconds. You'd expect it to reach 45 meters after 3 seconds, so an answer around maybe 40 or 41 meters is in the ball park. This approach is excellent for multiple choice questions, like the MCAT, but terrible for fill-in-the-blank questions.

 

[katezilla2]

Great! Thank you!

 

[Thoroughbred_Med]

I LOVED THIS SHORTCUT!

It has been a great help to me this summer while studying and I use it whenever possible in free fall questions!!!!!!

y=5t^2

Vf=10t