How Do You Write Position Vectors in Unit Vector Notation?

[Kieran Hughes]

Homework Statement

A steel ball is fired from a ballistic launcher at different angles. The launched ball has been found to travel from the edge of a table to land 30.0 cm from the far end of the table when starting from the height of the table and launched at an angle of 30.0◦ above the horizontal. When launched at 45.0◦ , the ball easily clears the table to land on the floor.
Letting the edge of the table from which the ball was launched have coordinates (x(0),y(0))=(0,0), write an expression for the x and y components of the object’s position vector. Next, write an expression for the full position vector.
I am trying to figure out how to write this expression. Underneath this explanation on my sheet I have a rx,30◦=x30◦=______, and a ry,30◦=y30◦=_______ and below that r(with -> on top)30◦(t)=______. I am confused as to write this, including the i-hats and j-hats unit vectors.

Homework Equations

N/A

The Attempt at a Solution

I understand the break down such as A = Ax + Ay = Axi + Ayj and so on, but where to put the numbers 0 and such are confusing me. I hope this format is correct for the forum!

 

[DrClaude]

I am trying to figure out how to write this expression. Underneath this explanation on my sheet I have a rx,30◦=x30◦=______, and a ry,30◦=y30◦=_______ and below that r(with -> on top)30◦(t)=______. I am confused as to write this, including the i-hats and j-hats unit vectors.

First write the expression in x, then in y, then combine both using $\hat{\imath}$ and $\hat{\jmath}$.

I understand the break down such as A = Ax + Ay = Axi + Ayj and so on, but where to put the numbers 0 and such are confusing me. I hope this format is correct for the forum!

If you start with the individual components, you won't have to worry aobut the zeros. But you can also write a zero as $0\hat{\imath} + 0\hat{\jmath}$.