Question

Gravity acceleration in lecture 2:

Instructor writes 80-5T^2 meters. . .

I can't wrap my mind around why it is not 80-10t^2 meters . . .

what am I missing? Isn't gravity 9.8m/s/s?

Thanks!

Answer 1

It is not explained, just given...the notes say:

The equation of motion for objects near the earth's surface (which we will just accept for now) says that the height above the ground h of het pumpkin t seconds after it's dropped from the building is roughly: ....h=80-5t^2 meters.

I'm no expert in physics, hardly had any ;)
But I can imagine gravity formulas being different for different objects (due to weight/form/etc). So maybe this is just what they calculated for a pumpkin?

Greetings,
Linda

Answer 2

I like the theory, but all objects fall at the same rate. So, it wouldn't be different for a pumpkin than anything else. Galileo and Newton beat this idea to death hundreds of years ago.

Consequently, here is a link to me launching pumpkins into the air:
http://www.youtube.com/watch?v=AWfyvWsa3zc

He said something about the derivative of 5t^2=10t, which is close to 9.8m/s, but is still not 9.8m/s/s. I'm just missing some mathematical insight he must be using which is probably one of the basic keys you have to get early on, and everyone takes it for granted.

Answer 3

They did translate the height to an "close to" 80 meters...perhaps they translated the gravity of 9.8 to 10 for the same reason? To keep the example "simple".

Or maybe someone else has a better explanation :)

Greetings,
Linda

Answer 4

-5t^2 is the position function. The derivative -10t is the velocity function. The derivative of the velocity -10 is the acceleration function. Which you notice is a constant. This is the -9.8 m/s/s that represents the constant acceleration of gravity. They rounded it to -10 for approximation purposes since they are teaching derivatives in calculus rather than mechanics in physics I.

Answer 5

So to clarify, at t=1, gravity is constant at -10 m/s/s, velocity is -10x1=-10m/s, and position is -5x1x1=-5m; at t=2, gravity remains constant at -10 m/s/s, velocity is now -10x2 = -20m/s, and position is -5x2x2 = -20m; at t=3, -10m/s/s, -30m/s, -45m. Remember they rounded -9.8 to -10 to simplify the math in the example.

Answer 6

The formula for the distance traveled under the force of gravity is 0.5*g*t^2 or 1/2 * g * t^2. (g being the gravitational constant. When one combines 0.5 and g one gets 4.9 (close to 5). The 80 apparently was the height from which the object was dropp

Answer 7

thanks for all the responses.