Question

knowledge
for each question, select the best answer from the four alternatives.

1. which of the following terms is used to describe the vector that is generated when adding two vectors?

(2.1)
(a) compass vector
(b) resultant vector
(c) diagonal vector
(d) general vector

1. which vector direction is equivalent to n 40° w?

(2.1)
(a) n 50° w
(b) n 50° e
(c) e 50° n
(d) w 50° n

1. for a diagram scale of 1 cm : 10 m, what is the real - world measurement of a 2.5 cm diagram measurement? (2.1)

(a) 2.5 m
(b) 25 m
(c) 25 cm
(d) 250 m

1. what distance does the vector in figure 1 represent in real life? (2.1)

scale 1 cm : 50 m
figure 1
(a) 110 m
(b) 110 cm
(c) 2.2 m
(d) 2.2 km

1. what is the x - component of the displacement vector δd₁ = 24 m s 22° e? (2.2)

(a) 9.7 m s
(b) 9.0 m e
(c) 22 m e
(d) 22 m s

Explanation:

Step1: Recall vector - addition terminology

The vector obtained by adding two vectors is called the resultant vector.

Step2: Analyze compass - direction equivalence

N 40° W means 40° west of north. W 50° N means 50° north of west, which is equivalent to N 40° W.

Step3: Use scale for real - world measurement

Given a scale of 1 cm : 10 m, for a 2.5 cm diagram measurement, the real - world measurement is \(2.5\times10 = 25\) m.

Step4: Use scale to find real - life distance

Given a scale of 1 cm : 50 m, if the vector length on the diagram is 2.2 cm (assumed from the context as no length is given in the question but needed to use the scale), the real - life distance is \(2.2\times50=110\) m.

Step5: Calculate x - component of displacement vector

For a vector \(\vec{A}=A\) with magnitude \(A = 24\) m and direction \(\theta = 22^{\circ}\) east of south, the x - component \(A_x=-A\sin\theta=- 24\sin(22^{\circ})\approx - 9.0\) m (negative because it is in the east - west direction and towards the east).

Answer:

1. B. resultant vector
2. D. W 50° N
3. B. 25 m
4. A. 110 m
5. B. 9.0 m (E)