Solve Vector Problems - Check My Answers Correct?

[AznBoi]

I have a few vector problems that I'm unsure of. I have an answer for them but I don't know if it is correct. Please help check. Thanks.

#1 A jogger runs 100m due west, then changes direction for the second leg of the run. At the end of the run she is 175m away from the starting point at an angle of 15 degree north of west. What were the direction and length of her second displacement? Use graphical techniques.

My answer: Direction-33 degree North of West.

#2 The displacement vectors A and B each have a magnitude of 3m. Vector B starts from the origin to the positive y direction. Vector A starts from the origin to the positive x direction (30 degrees N of E). Graphically find a) A+B; b) A-B; c) B-A; d) A-2B

My Answers:
a) Magnitude of 5.2 at +60 degrees.
b) Magnitude of 3m at -30 degrees.
c) Magnitude of 3m at +150 degrees.
d) Magnitude of 5.2m at -60 degrees.

I don't know if I wrote my answers correctly. Do I need to add the direction too? for example Magnitude of 5.2 at +60 degrees N of W??

#3 A quarterback takes the ball from the line of scrimmage, runs backward for 10yds. and the runs to the right parallel to the line of scrimmage for 15yds. At this point he throws a 50 yd. forward pass straight down field, perpendicular to the line of scrimmage. What is the magnitude of the football's resultant displacement?

My Answer:
Magnitude of the football's resultant displacement: 42.5 yds. at +70 degrees.

Btw what does Magnitude of 3m mean? Magnitude of the football's resultant displacement? Magnitude just means the number right?

Thanks a LOT!

 

[OlderDan]

I have a few vector problems that I'm unsure of. I have an answer for them but I don't know if it is correct. Please help check. Thanks.

#1 A jogger runs 100m due west, then changes direction for the second leg of the run. At the end of the run she is 175m away from the starting point at an angle of 15 degree north of west. What were the direction and length of her second displacement? Use graphical techniques.

My answer: Direction-33 degree North of West.

What about the length?

#2 The displacement vectors A and B each have a magnitude of 3m. Vector B starts from the origin to the positive y direction. Vector A starts from the origin to the positive x direction (30 degrees N of E). Graphically find a) A+B; b) A-B; c) B-A; d) A-2B

My Answers:
a) Magnitude of 5.2 at +60 degrees.
b) Magnitude of 3m at -30 degrees.
c) Magnitude of 3m at +150 degrees.
d) Magnitude of 5.2m at -60 degrees.

I don't know if I wrote my answers correctly. Do I need to add the direction too? for example Magnitude of 5.2 at +60 degrees N of W??

Assuming x and y directions are perpendicular axes, these answers are not correct whether expressed relative to compass points or the axes.

#3 A quarterback takes the ball from the line of scrimmage, runs backward for 10yds. and the runs to the right parallel to the line of scrimmage for 15yds. At this point he throws a 50 yd. forward pass straight down field, perpendicular to the line of scrimmage. What is the magnitude of the football's resultant displacement?

My Answer:
Magnitude of the football's resultant displacement: 42.5 yds. at +70 degrees.

You were only asked for the magnitude. 42.5 is close. 42.7 is closer

Btw what does Magnitude of 3m mean? Magnitude of the football's resultant displacement? Magnitude just means the number right?[/U]

Yes, magnitude is the number associated with the vector. For displacement, the magnitude is the distance, The magnitude of 3m means the length of the displacement vector. There is no way you can add or subtract two perpendicular vectors of 3m length and get your results in #2.

 

[AznBoi]

how come the answers in #2 are wrong? I used graphical methods, 1m=1/2cm and I used the daisy chain method. I connected vector B to the tip of vector A and found the resultant vector. Isn't that right?

 

[AznBoi]

oh for #1 I got 82m, direction 33 degrees N of W

 

[OlderDan]

how come the answers in #2 are wrong? I used graphical methods, 1m=1/2cm and I used the daisy chain method. I connected vector B to the tip of vector A and found the resultant vector. Isn't that right?

This may be a matter of interpretation. What do you consider to be the y direction? If the positive x direction is 30 degrees N of E, and x and y are the axes of a Cartesian coordinate system, then the positive y direction is 30 degrees W of N. If you have two vectors of the same magnitude at right angles to one another, no matter how you add or subtract them the resulting magnitude will be the same, and it will certainly not be the length of one of the original vectors. I think you are assuming x and y are not perpendicular, which I think is incorrect unless you have something specifically stating they are not.

 

[AznBoi]

Ok the Vector B is on the y-axis It goes straight upward from the origin, 3m. Vector A is 30 degrees N of E, like a diagonal line pointing in the NE direction. Sorry it's kind of hard to explain the vectors without a visual.
Now would my answers be correct? Thanks. :tongue:

 

[OlderDan]

Ok the Vector B is on the y-axis It goes straight upward from the origin, 3m. Vector A is 30 degrees N of E, like a diagonal line pointing in the NE direction. Sorry it's kind of hard to explain the vectors without a visual.
Now would my answers be correct? Thanks. :tongue:

So the original vectors A and B have a 60 degree angle between them. Your answers are OK if your angles are measured relative to East.

The non-standard use of x in y in the original statement of the problem is confusing.

 

[AznBoi]

Yes the vectors are 60 degress apart from each other and they are both in the
1st quadrant.

What do you mean my answers are ok?? Do I need to add the direction (i.e. N of E) to my answers?? Are the degrees that I have close to being right? I'm kind of confused about the -degree and +degrees. I used a ruler and protractor to graph these vectors so yeah. =P Thanks :tongue:

 

[OlderDan]

Yes the vectors are 60 degress apart from each other and they are both in the
1st quadrant.

What do you mean my answers are ok?? Do I need to add the direction (i.e. N of E) to my answers?? Are the degrees that I have close to being right? I'm kind of confused about the -degree and +degrees. I used a ruler and protractor to graph these vectors so yeah. =P Thanks :tongue:

There is a mathematical convention that, unless otherwise spedified, the positive x-axis is horizontal to the right and the positive y-axis is vertical and upward. This corresponds to East and North on a map. Another convention is that direction angles are measured relative to the positive x-axis with positive angles as a counterclockwise rotation and negative as a clockwise rotation. So angles between 0 and +90 are related to the first quadrant, and angles between 0 and -90 are related to the fourth quadrant, etc. Except for that initial reference to the x-axis pointing 30 degree N of E, your answers would be perfectly clear. If there is an x-axis in that direction, then your answers should be explicit about your reference axis. Are your directions relative to East, or to some x-axis in some other direction? It would not hurt to express your answers in terms of compass directions.

 

[AznBoi]

Alright I understand now, thanks a bunch! :tongue: