# Vector – problems and solutions

**Vector and Scalar**

1. Among the following options, which are scalar-vector pairs…

A. Force – acceleration

B. Pressure – force

C. Displacement – speed

D. Electric current – pressure

Solution :

Force = vector, acceleration = vector

Pressure = scalar, force = vector

Displacement = vector, speed = scalar

Electric current = scalar, pressure = scalar

The correct answer is B.

2.

The correct answer is shown by number…

A. 1 and 4

B. 1 and 2

C. 2 and 3

D. 3 and 4

Solution :

Speed = scalar

Displacement = vector

Weight = vector

Acceleration = vector

The correct answer is C.

**Components of vectors**

3. Two vectors, F_{1} = 20 N and F_{2} = 30 N, have direction as shown in the figure below. Determine the resultant of components of vectors in x-axis and y-axis.

A. 5√3 N and -25 N

B. -5√3 N and 25 N

C. 25 N and 5√3 N

D. 30 N and 25√3 N

__Known :__

F_{1} = 20 Newton

Angle between F_{1} and x axis = 30^{o}

F_{2} = 30 Newton

Angle between F_{2} and x axis =30^{o}

__Wanted :__ F_{x }and F_{y}

__Solution :__

F_{1x} = F_{1} cos 30^{o} = (20)(0.5√3) = 10√3 Newton (plus sign because points to +x axis)

F_{1y} = F_{1} sin 30^{o} = (20)(0.5) = 10 Newton (plus sign because point to +y axis)

F_{2x} = F_{2} cos 30^{o} = (30)(0.5√3) = -15√3 Newton (minus sign because points to -x axis)

F_{2y} = F_{2} sin 30^{o} = (30)(0.5) = 15 Newton (plus sign because points to +y axis)

The resultant of the x component :

F_{x} = F_{1x} + F_{2x} = 10√3 N – 15√3 N = -5√3 Newton

The resultant of the y component :

F_{y} = F_{1y }+ F_{2y} = 10 N + 15 N = 25 Newton

The correct answer is B.

**The resultant of two vectors**

4. Two children A and B push a block, if A push the block southward with force of 400 N and at the same time B push the block eastward with force of 300 N, then determine the resultant of force A and B.

A. 100 N southward

B. 100 N eastward

C. 500 N southeastward

D. 700 N southeastward

__Known :__

U = north, T = east, S = south, B = west

TL = northeast, TG = southeast, BD = southwest, BL = northwest

A = 400 Newton southward

B = 300 Newton eastward

__Wanted:__ magnitude and direction of net force (R)

__Solution :__

The correct answer is C.

**The resultant of the vector of displacement**

5. Someone riding a motorcycle from home 6 km to north then 8 km to east. Determine the final position of the person from the initial position.

A. 14 km northeast

B. 14 km southwest

C. 10 km northeast

D. 10 km northwest

__Known :__

__Wanted:__ magnitude and direction of the resultant of displacement

__Solution :__

The correct answer is C.

6.

Based on the figure above, If 1 square represents 1 km, then what is the total displacement.

Solution :

Distance = A + B + C = 6 + 6 + 2 = 14 km

Displacement = R = 12 km

7. A car travels from A to B along 30 km north, then 60 km east, then 110 km south. Determine the displacement of the car from A to D.

Solution :

AA’ = 60 km

A’D = 110 km – 30 km = 80 km

8. A car travels from town A to town B 100 km north, then to town C 60 km east, and then to town D 20 km south. Determine the displacement of the car.

Solution :

D’D = 60 km

AD’ = 100 km – 20 km = 80 km