An alternative solution to the Boat heading across the river problem

Last time I set up two equations in two unknowns (theta and v), eliminated v and then had Wolframalpha solve for theta.

Another approach, illustrated below, gives an analytical solution for v, which can then get plugged in to get theta.
I mentioned this as a possible solution in class today but hadn't worked it out.
Here it is:


Folks in my TuTh class seemed at least intrigued by the log-log linearization of the period mass data and adjusting the "Mass of the tray" parameter until they get a perfect straight line. Hooray!

Bringing logger pro graphs into the blog

I had tried using Grab to capture a graph and paste it into the blog. Looking again at the first day's blog entry today I see that that didn't work.

This time I saved the Grab capture as a tiff (the default) and I'll try pasting that picture in:

So far it looks okay, even though it isn't one of the designated formats.

I open the .tiff with Preview and saved it as a .png, one of the favored formats. Here goes:

 

I'll have to check later so see if both "took".

 

First day of class material:

Vector addition
Set up an origin.
Walk 13 m at 22.62º North of East, then 10 m at 38.86º North of West.
Add by:
1) Taking components (set up x, y column for each vector, and a sum at the bottom). Note that the first vector is (12m, 5 m) and the second one is (-8m, 6 m). Use the Pythagorean theorem and arctan to get the magnitude and direction of the resultant vector.
2) Using the law of cosines to find the missing side (resultant), then the law of sines to find the angle between the 13 m vector and the resultant, then summing that with 22.62º to get the resultant angle (a lot more work!)
Both approaches give 11.7 m away at 70.0º north of east

Relative Velocities:

Consider three people's motion relative to you standing still:
A) John, moving 4 m/s North
B) Paul, moving 6 m/s East
C) George, moving 7.21 m/s at 33.69º (which happens to be the sum of 4 m/s north and 6 m/s east)



1) On your whiteboards, figure out what each of the following looks like:
a) v_Paul relative to John (so, how John see's Paul's velocity)
b) v_John relative to Paul
c) v_George relative to Paul
d) v_Paul relative to George
e) v_John relative to George
f) v_ George relative to Paul

2) Convince yourself by choosing pairs of vectors above that it is always true that:
         v_(A rel to B) + v_(B rel to C) = v_(A rel to C)

3) Consider a river flowing 3 m/s north.
    You have a boat that can go 7 m/s relative to the water.
    Find the direction to point the boat such that it follows a direct route to a point on the opposite shore along a line 10º north of west from your original route.

      Note that we have v_boat rel to water   and    v_water relative to ground
      We want v_boat relative to ground to point 10º North of east. 

   Which way do we point? Consider first pointing the boat directly across the river.

    So we have to point the boat south somewhat. The situation looks like this:
        


   Set up the x and y equations for the velocity.


Go to www.wolframalpha.com. Type in   solve -7sinx+3=1.2343cos x
then hit the = sign. Find the solution that looks to be around 10-15º, keeping in mind that computers always use radians for their answers!

From here we went to setting up and collecting data and talking through the analysis for the Inertia Balance lab.

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