# 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?

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!

## 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)

?

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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.

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.