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 (vx) = 2 m/s

The vertical component of the velocity (vy) = 1.5 m/s

Time interval (t) = 4 seconds

Wanted : Displacement

Solution :

The resultant of the velocity (v) :

Unit vector – problems and solutions 1

Displacement :

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

s = 10 meters

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

Unit vector – problems and solutions 2

Solution :

Unit vector – problems and solutions 3The components of vectors :

F1x = (F1)(cos 60o) = (14)(0.5) = -7 N (Negative because this vector component points along the negative x axis (leftward))

F1y = (F1)(sin 60o) = (14)(0.53) = 73 N (Positive because this vector component points along the positive y axis (rightward))

F2x = 10 N

F2y = 0

The components of the resultant vectors :

Fx = F1x + F2x + F3x = -7 + 10 = 3 N

Fy = F1y + F2y + F3y = 73 + 0 = 73 N

The resultant vector in unit vector :

R = 3 i + 73 j

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