Physics Lab - Projectile Motion - Deriving a Position Vector

[Ahwleung]

Homework Statement

Okay, this lab has had me stumped for the last few hours. This is our first lab for AP Physics BC.

Problem: Determine the position vector that describes the locatino of the water that is launched by a drinking fountain. Your position vector needs to be in unit vector format (i, j, k) & will include the variable t (t=0 when the water droplet is at the spout). Also determine the velocity vector, the acceleration vector, the initial velocity, the initial launch angle, and the minimum speed of the water (which is 0 at the top because the water goes up, then down)

My thoughts: It's just two dimensions so no k variable and we were only allowed to use a ruler, no stopwatches or anything else so I assume you solve for t in the equations later on. Just in case, we used cell phone timers and got t = 2.1 seconds. The Origin (0,0) is at the left edge of the drinking fountain.

The measurements are kind of complicated, so I'll just put them into a paint file.

Homework Equations

We did a problem involving vectors in which we used the equation (parenthesis = subscript)
r(f) = r(i) + v(i)*t + .5a(t^2)
So I assume you must find out r(i), v(i), change in time, and "a" (acceleration)

The Attempt at a Solution

This is the part that has me stumped. At first, the answer seems kind of obvious. Looking at the green vector, the component parts are clear (change in x = -.23 m, change in y = -.05 m) and thus the position vector is -.23i -.05j. But from there, how would one go about finding all the other answers? Heres my thoughts on the other vectors.

Velocity Vector: I'm not sure what they are asking for. Are they asking for the velocity of the water in a vector format, or the velocity of the position vector?

Acceleration Vector: Is it possible to derive a vector? Could I just derive the position vector to find velocity and derive again to find acceleration?

Initial velocity: Apparently I have to resort to the old kinematics equation to find initial velocity.

Initial Launch Angle: Now this part has me worried. I don't think you can solve for it in an equation; were we supposed to measure how HIGH the water went and do a simple tangent equation?

The minimum speed: easy, it's 0 because the velocity goes from positive to negative and thus must hit 0 at some point (like throwing a ball into the air and catching it). Or is it not that easy because the water is moving in the x direction?


Sorry for this outrageously long post. I've been staring at this lab for hours and I can't seem to make any headway into it. Thanks ahead of time for your consideration.

 

[Ahwleung]

As a side note/funny little story, our physics teacher claimed that he DREAMED of this lab; he wanted to show us that with a ruler and a little brainwork you can solve for anything.

He also said that our final would be to find the air pressure of the room with only a ruler, a compass, and a piece of scotch tape.

 

[Ahwleung]

I've found that the acceleration is -9.8j because its gravity...

 

[andrevdh]

I think one should strart by trying to discover whether the stream is following a parabolic trajectory. This could be investigated by marking the position of the stream on a plastic sheet (transparency) held next to the stream. Mark its position by holding the sheet between you and the stream. I think what he wants you to do is describe the position coordinates of a droplet of water as is traveling along the stream (as a function of time). It is probably best to locate the origin at the exit point of the water (by viewing the stream from the other side than that in your drawing it flows left to right). If you are just suppose to use a ruler this can still be achieved but with more effort. In such case you need to measure both the x- and y-coordinates of the stream. Map a line at constant intervals in the basin along the x-axis and then measure the y-coords of the stream up from these points.