Given: The magnitude of position vector r = r = 78 m
The angle relative to the x-axis θ =30°
Concept: If the position vector r making angle θ with x-axis then position vector can be expressed as
r = r cos θ i + r sin θ j
Here, i and j are the unit vectors along x and y axes respectively.
x component of position vector r = r cos θ
y component of position vector r = r sin θ
Solution: From the given problem, the position vector r can be written as
r = (78 cos 30° i + 78 sin 30° j ) m
So, the x component of position vector r = 78 cos 30° m = 67.55 m
And, the y component of position vector r = 78 sin 30° m = 39.0 m
Hence, the required x & y components of position vector r will 67.55 m and 39.0 m respectively.
