Drawing a free body diagram for vectors

[shayaan_musta]

I have some question related to vectors.

1)How will you find a vector(A) if you given another vector(B) in +x-direction to give a resultant(R) at θ(any degree)?

2)A child is holding a wagon from rolling straight back down a driveway that is inclined at 20° to horizontal. If the wagon weighs 150N, with what force must the child pull on the handle if the handle is at 30° above the incline?(This question is asked by a friend. I tried but I am not able to get answer. I told him that I will ask an expert then tell you.)

3)Find the magnitude and angle of R if R=7.0i-12j
I did not get to angle, my θ=-1.042. Is my answer wrong?

Last question
4)If you give a vector in form of its magnitude and ask to write it in the form of unit vectors(i,j,k) then how will do it?

Any help is appreciable. Thanks in advance.

 

[berkeman]

I have some question related to vectors.

1)How will you find a vector(A) if you given another vector(B) in +x-direction to give a resultant(R) at θ(any degree)?

2)A child is holding a wagon from rolling straight back down a driveway that is inclined at 20° to horizontal. If the wagon weighs 150N, with what force must the child pull on the handle if the handle is at 30° above the incline?(This question is asked by a friend. I tried but I am not able to get answer. I told him that I will ask an expert then tell you.)

3)Find the magnitude and angle of R if R=7.0i-12j
I did not get to angle, my θ=-1.042. Is my answer wrong?

Last question
4)If you give a vector in form of its magnitude and ask to write it in the form of unit vectors(i,j,k) then how will do it?

Any help is appreciable. Thanks in advance.

[1] Use trigonometry. Can you draw us a sketch?

[2] Start by drawing a free body diagram (FBD). Can you draw that for us, and label the forces on it?

[3] Show us your math. Is your answer in radians?

[4] Use polar to rectangular conversion formulas:

http://en.wikipedia.org/wiki/Polar_coordinate_system

.

 

[shayaan_musta]

[1] Use trigonometry. Can you draw us a sketch?

[2] Start by drawing a free body diagram (FBD). Can you draw that for us, and label the forces on it?

[3] Show us your math. Is your answer in radians?

[4] Use polar to rectangular conversion formulas:

http://en.wikipedia.org/wiki/Polar_coordinate_system

.

1)Here is an example question for what I am asking you.
What displacement must be added to a 50cm displacement in the +x-direction to give a resultant displacement of 85cm at 25°?

2)Here is link that I try to made a sketch for question 2.Please check it.
http://s1227.photobucket.com/albums/ee430/Shayaan_Mustafa/Album%201/?action=view&current=untitled.jpg

3)I am using θ=tanˉ¹(y/x)
θ=tanˉ¹(-12/7)
θ=-1.042°(in degree not radian)
But my answer is wrong.
Correct is θ=60°. How?

4)Ok thanks I got link.

 

[tiny-tim]

3)I am using θ=tanˉ¹(y/x)
θ=tanˉ¹(-12/7)
θ=-1.042°(in degree not radian)
But my answer is wrong.
Correct is θ=60°. How?

it's 1.042 radians …

i think you pressed the wrong button on your calculator!

 

[shayaan_musta]

it's 1.042 radians …

i think you pressed the wrong button on your calculator!

Ok ok thanks. I was wrong. Thanks to help me.