Answer to Question #169049 in Physics for Samuel Mkandawire

Question

1. Physical quantities are categorized as either scalar or vector. With clear examples, discuss the feature which differentiates them.

2. Clearly explain the meaning of the term resultant vector.

3. From Lecture theater 2, Mr. Nkonde moves 80m east along the sheltered walk path way and then 125m south to the university library. Find the displacement of Mr Nkonde.

4. To go from the student hostels to the university library, a student must cover 650m in a direction 47o south of west. To go from the football ground to the library, the student must move straight south for 420m. How far and in what direction must the student move to go from hostels to the football ground?

5. Mr. Kazhimaika gives a map to a first student studying Fisheries and Aquaculture so that she gets to the new fish ponds. The map says, ‘start from the central administration car park, go 125m straight north, then 200m at 45o north of east, then 150m straight east, and finally, 30m at 30o east of south’. How far from the central administration car park and in what direction are the fish ponds?

6. In map – work exercise, hikers are required to walk from a tree mark A on the map to another marked B which lies 5.0km due east of A. The hikers then will have to walk in a straight line to a waterfall in position C which has a component measured from B of 2.0km east and 6.0km north.

(i) Draw a clearly labeled displacement – vector diagram of the route the hikers would take to complete the journey.

(ii) What would be the total distance to be covered by the hikers?

7. Four forces, 60N at 60o and 50N at 30o both clockwise, 50N at 30o, 40N due north – west and 30N south – west, act at the origin. Calculate the magnitude and direction of the resultant force.

8. The diagram below shows three ropes F1= 450N, F2= 300N and F3= 600N hooked from the same hook as they support the roof. Resolve each force acting on the hook into its x and y components.

12. Determine the magnitudes of the following vectors;

(i) 𝑨⃗⃗ =(𝟐𝒊̂+𝟑𝒋̂+𝟔𝒌̂)

(ii) 𝑩⃗⃗ =(𝟑𝒊̂+𝟗𝒋̂−𝟔𝒌̂)

(iii) 𝑪⃗⃗ =(𝟑𝒊̂−𝟓𝒋̂+𝒌̂)

(iv) 𝑫⃗⃗ =(𝟖𝒊̂−𝟒𝒋̂+𝟖𝒌̂)

13. Find the angle between the vectors 𝑨⃗⃗ =(𝟑𝒊̂+𝟐𝒋̂+𝒌̂) and 𝑨⃗⃗ =(𝟓𝒊̂−𝟐𝒋̂−𝟑𝒌̂)

14. Prove that following vectors are perpendicular to each other

(i) 𝑨⃗⃗ =(𝒊̂+𝟐𝒋̂+𝟑𝒌̂) and 𝑩⃗⃗ =(𝟐𝒊̂−𝒋̂)

(ii) 𝑪⃗⃗ =(𝟑𝒊̂−𝟐𝒋̂+𝟖𝒌̂) and 𝑫⃗⃗ =(𝟐𝒊̂+𝟐𝒋̂−𝟏𝟒𝒌̂)

(iii) 𝑬⃗⃗ =(𝟏𝟖𝒊̂+𝟔𝒋̂+𝟔𝒌̂) and 𝑭⃗⃗ =(−𝟐𝒊̂+𝟑𝒋̂+𝟑𝒌̂)

(iv) 𝑮⃗⃗ =(−𝟔𝒊̂+𝟑𝟒𝒌̂) and 𝑯⃗⃗⃗ =(𝟏𝟐𝒊̂+𝟐𝟑𝒋̂+𝟒𝒌̂)

15. Determine the value of a so that vector 𝑨⃗⃗ =(𝟏𝟎𝒊̂+𝟏𝟒𝒋̂−𝟔𝒌̂) is perpendicular to vector 𝑨⃗⃗ =(𝟏𝟐𝒊̂+𝟏𝟐𝒋̂+𝒂𝒌̂)

16. A particle covers a distance of (𝟐𝒊̂+𝟑𝒋̂+𝟓𝒌̂) metres in the direction of a constant force of (𝟕𝒊̂+𝟖𝒋̂+𝟑𝒌̂) newtons acting on it. Calculate the work done by the force on this particle.

17. A body moves from position (𝟐𝒊̂+𝟐𝟎𝒋̂−𝟏𝟖𝒌̂) metres to a position

(𝟏𝟔𝒊̂+𝟐𝟒𝒋̂+𝟏𝟓𝒌̂) metres when a force of (𝟒𝒊̂+𝟐𝒋̂+𝟑𝒌̂) newton is applied on it. Calculate the work done on a body.

18. A point of application of a force 𝑭⃗⃗ =(𝟏𝟔𝒊̂+𝟐𝟎𝒋̂+𝟏𝟓𝒌̂) is moved from

𝒓𝟏⃗⃗⃗⃗ =(𝟐𝒊̂+𝟕𝒋̂+𝟐𝒌̂) to 𝒓𝟐⃗⃗⃗⃗ =(𝟓𝒊̂+𝟏𝟐𝒋̂+𝟑𝒌̂). Find the work done.

Answer 1

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