I need help with my physics lab. projectile motion lab on an air table that was tilted. the puck was projected (pushed once) across the table in a projectile manor and dots were made with a spark timer on a piece of paper. the dots were recorded as x,y, and time in tables. We have to find the horizontal velocity and acceleration and graphing it. can someone tell me how to do it? I was thinking of using derivatives to find the v-t but, i need to prove that what i have is a parabola(quadratic) how do i prove it?

Question

I need help with my physics lab.  projectile motion lab on an air table that was tilted. the puck was projected (pushed once) across the table in a projectile manor and dots were made with a spark timer on a piece of paper. the dots were recorded as x,y, and time in tables. We have to find the horizontal velocity and acceleration and graphing it. can someone tell me how to do it? I was thinking of using derivatives to find the v-t but, i need to prove that what i have is a parabola(quadratic) how do i prove it?

anonymous · Answer

For something to move in a projectile motion, it's got to have a constant force acting on it, thus having a constant acceleration.  Gravity would be a common example of such a constant force.

anonymous · Answer

When you have constant acceleration $a$, then you integrate twice to get position $s(t)$: $$
s(t)=\iint a\,dt^2 = \int at+C_1dt = \frac{a}{2}t^2+C_1t+C_2
$$

buggiethebug · Answer

no calculus please :(
We broke it into components and now we have to work with components to find the vertical and horizontal graphs

anonymous · Answer

"I was thinking of using derivatives"
"no calculus please :("
Do as you say, not as you do?

anonymous · Answer

Look, if you find $\Delta s/\Delta t$ you get average velocity.  If you then do $\Delta \overline{v}/\Delta t$ you'll get average acceleration.  If you show acceleration is constant, then you know it's parabolic motion...

anonymous · Answer

But that relationship between parabolic motion and constant acceleration comes from calculus.

buggiethebug · Answer

no...i meant no integrals i have no idea what those are lol

anonymous · Answer

They're the inverse of derivatives.

buggiethebug · Answer

but our teacher doesn't want us to calculuate, he wants us to use graphs, but to find the equation we have to give proof why it's parabolic and not quartic you know what i mean?

buggiethebug · Answer

wait what do we need the inverse of the derivatives for in this situation?

anonymous · Answer

Okay how about this...
Start with $$
s(t) = at^2+bt+c\
v(t) = s'(t) = 2at+b\
a(t) = s''(t) = 2a
$$Proves if it is parabolic then it must have constant acceleration, but not necessarily the converse...

buggiethebug · Answer

constant acceleration in the x or y?