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) :
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 :
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)(0.5√3) = 7√3 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 = 7√3 + 0 = 7√3 N
The resultant vector in unit vector :
R = 3 i + 7√3 j