Question

The position vectors particle has length 1m and makes 30° with the x-axis. What are the lengths of the x and y components of the position vector?

Answer 1

Let OA is position vector of particle has length 1m and makes 30° with the x - axis. In attachment it is clearly shown .

In figure OB is the component of OA along x axis.
and OD is the component of OA along y - axis.

In ∆OAB ,
Apply , cos30° = OB/OA
OB = OAcos30° = 1 × √3/2 = 1.732/2 = 0.866 m
Similarly, sin30° = AB/OA
∵ AB = OD
So, sin30° = OD/OA
OD = OAsin30° = 1 × 1/2 = 0.5 m

Hence, component of OA along x- axis = 0.866 m
Component of OA along y-axis = 0.5 m

Answer 2

Hi mate

Refer the attachment

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