Graphical Techniques for Vector Displacement and Magnitude Calculations

[wtf_albino]

2) A roller-coaster moves 200 ft horizontally, then rises 135 ft at an angle of 30.0 degrees above the horizontal. It then travels 135 feet at an angle of 40.0 degrees below the horizontal. Use graphical techniques to find its displacement from the starting point at the end of this movement.


I feel like such an idiot! I don't even know how to draw this thing out! My attempt is attached.



How would you solve this graphically? In my class today my teacher told us that we wouldn't have to use the Law of Cosines or Law of Sines and just be able to use simple trig to figure it out. However, there are no 90 degree angles to work with. I've been working on this thing for almost 40 minutes and this is the best i can do damn..





2) Vector A is 3.00 units in length and points along the positive x-axis. Vector B is 4.00 units in length and points along the negative Y-axis. Use graphical methods to find the magnitude and direction of the vectors. A) A + B and (b) A - B


I have attached my attempt.



3) A jogger runs 100 m due west, then changes direction for the second leg of the run. At the end of the run, she is 175 m away from the starting point at an angle of 15.0 Degrees north of west. What were the direction and length of her second displacement? Use graphical techniques.


My drawing attempt is attached.


For this problem.. i don't really see another way of coming up with the answer unless i use the law of sins. My teacher specifically told us not to though.. he said these questions could be done with simple trig. I have no idea what he's talking about though, i think I am just an idiot

 

[wtf_albino]

anyone?.. help would be very much appreciated.

 

[wtf_albino]

no one?

 

[wtf_albino]

losing hope..

 

[fujiwara_sai]

let me try

for qns 1:
Choose a scale for ur ruler like 1cm of ruler:10ft/20ft/30ft. Choose what you deem fit.
Then, draw the diagram using ruler and protractor
Join starting point to ending point and you should get ur displacement.

qns 2:
try the tactic from 1

qns 3:
tactic from 1 should get you ur answer if you draw nicely the diagrams

 

[HallsofIvy]

First, understand that most people tend to look at this board once every couple of days. There is not a group of people waiting anxiously in an office for questions to come in!

What you did for the first problem looks good except that it doesn't look, to me, like your two "135 foot lengths" are the same!
(I wrote the following before looking at your diagrams.)
"A roller-coaster moves 200 ft horizontally" Okay, draw a horizontal line and mark off "200 ft" (at whatever scale is convenient).

"then rises 135 ft at an angle of 30.0 degrees above the horizontal."
At the end of your horizontal line measure a 30 degree angle upward.
Extend that line to a length of 135 feet (in scale).
It is possible to interpret "rises 135 ft" to mean 135 feet measured vertically but because of the next line I don't believe that is meant.

"It then travels 135 feet at an angle of 40.0 degrees below the horizontal."
"Travels 135 feet" clearly means the length is 135 ft.
At the point you just end that line at, measure an angle 40 degrees downward. Extend that line to 135 feet (in scale). Finally, measure the straight line distance between your beginning and ending points. That, together with the angle that line makes with the horizontal, is the "displacement"

Problem number 2 looks good.

In the third problem, your 15 degrees is in the wrong place. The direction to the final point from the initial point is "15 degrees north of west". That means that the angle at the initial point is 15 degrees up from the horizontal (the horizontal is "west" and up is "north"). Draw the picture in scale and measure the length and angle of the second leg.

 

[wtf_albino]

ah thanks a lot halls, i understand now