Find the x and y components of a position vector r⃗, of magnitude r = 78 m, if its angle relative to the x axis is 30.0 ∘.

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.