Vector Notation with force and displacement help. Thanks

[nukeman]

Homework Statement

This is not a homework question, but rather a review question. I have the answer, ill post below, but have no idea how to get to the answer :)

Question: "A constant force of 90.0N acts on a ball while it has a displacement of 1.40m at 10 degrees below the x-axis. The force makes and angle of 60 degrees with the x-axis, as shown in the figire (DO you guys need the figure to figure this out?)

A) Express the force, F, and the desplacement d, in unit vector notation?

The correct answer is:

F=(45 N i) + (77.9 N j)
d = (1.38 m)i - (0.243 m)j

Can anyone help me out on how to figure this out please?

THanks!

Homework Equations

The Attempt at a Solution

For F - Do I just go 90cos(60) = 45.0 N ? (Can you explain to me why I use COS for that one?

I guess what I am having trouble with is knowing which is i (sin or cos) and which is j (sin or cos)

?

 

[sandy.bridge]

For the force vector, draw it out. You know it is acting at 60 degrees relative to the x-axis, so that is a start. Next, resolve the vector into its components to hence determine the component in the x-direction and the component in the y-direction, which could make use of sine or cosine, depending which angle you use.

 

[LabGuy330]

I agree with sandy.bridge

if it makes it easier you can draw one coordinate x-y axis and have the ball displaced as mentioned from there and solve for displacement in horizontal (i) and vertical (j) direction.

then you can draw another coordinate x'-y' axis with the origin at the ball and draw the force vector from this axis and solve for the force in the horizontal (i) and vertical (j) direction.