# Unit vector – problems and solutions

1. An object moves at a velocity of v = (2i − 1.5j) m/s. What is the displacement of the object after 4 seconds?

__Known :__

The horizontal component of the velocity (v_{x}) = 2 m/s

The vertical component of the velocity (v_{y}) = 1.5 m/s

Time interval (t) = 4 seconds

__Wanted :__ Displacement

__Solution :__

The resultant of the velocity (v) :

Displacement :

s = v t = (2.5 m/s)(4 s)

s = 10 meters

2. Vector F_{1} = 14 N and F_{2} = 10 N. Determine the resultant vector if stated in R = i + j.

Solution :

The components of vectors :

F_{1x} = (F_{1})(cos 60^{o}) = (14)(0.5) = -7 N (Negative because this vector component points along the negative x axis (leftward))

F_{1y} = (F_{1})(sin 60^{o}) = (14)(0.5√3) = 7√3 N (Positive because this vector component points along the positive y axis (rightward))

F_{2x} = 10 N

F_{2y} = 0

__The components of the resultant vectors :__

F_{x} = F_{1x} + F_{2x} + F_{3x} = -7 + 10 = 3 N

F_{y} = F_{1y} + F_{2y} + F_{3y} = 7√3 + 0 = 7√3 N

__The resultant vector in unit vector :__

R = 3 i + 7√3 j