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

[irp]

2. Vector F₁ = 14 N and F₂ = 10 N. Determine the resultant vector if stated in R = i + j.

Solution :

The components of vectors :

F_1x = (F₁)(cos 60^o) = (14)(0.5) = -7 N (Negative because this vector component points along the negative x axis (leftward))

F_1y = (F₁)(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