Scalars and Vectors

Question 1

Name the 7 fundamental SI Units

Answer 1

Length
Mass
Time
Current
Temperature
Amount of substance
Luminous intensity

Question 2

What is a name for these examples?

Distance = 10m

Temperature = 274 K

Answer 2

Scalar quantities

Question 3

What is it called when a qauntity has a direction attached to it? Give example

Answer 3

A vector

Example: 15N to the right
Acceleration = 8ms^-2 north

Question 4

What can a vector be donoted with?

Answer 4

An arrow on the top or a bold type. Use the arrow method

Question 5

What is the vector component of a^→ in the y direction

Answer 5

a^→vy

Question 6

What is the vector component of a^→ in the x direction

Answer 6

a^→vx

Question 7

What can a vector be split into?

Answer 7

Two vectors called components

a^arrowvx and a^arrowvy

Question 8

How can the components be found?

Answer 8

Using the definitions of the sine and cosine functions

Question 9

What are the definitions of the sine and cosine functions?

Answer 9

avx = a cos(θ) and avy = a sin(θ)

Question 10

avx = a cos(θ) and avy = a sin(θ) What are these componants?

Answer 10

Perpendicular to each other

Question 11

A goal keeper kicks a ball at an angle of 30° from the horizontal and at a velocity of 5ms^-1. Assuming the ball travels perfectly in a straight line, calculate thex and y componants on the balls velocity.

Answer 11

x = 4.33ms^-1
y = 2.5ms^-1

Question 12

What is the method of finding componants called?

Answer 12

Vector resolution

Question 13

The X componant decreases to 3ms and y becomes 4ms. Velocity remains unchanged, calculate the new angle

Question 14

Can scalars and vectors be simply added or subtracted?

Answer 14

Vectors cannot because of their direction.

Question 15

How can vectors be added or subtracted to find the equivalent value or resultant?

Answer 15

A graphical approach can be used to add or subtract coplanar vectors(vectors in the same plane)

Question 16

How can vectors be added or subtracted to find the equivalent value or resultant?

Answer 16

A graphical approach can be used to add or subtract coplanar vectors(vectors in the same plane)

Question 17

What is subtracting and adding coplanar vectors known as?

Answer 17

Triangle law of vector addition

Question 18

How do you add 2 coplanar vectors a^→ and b^→

Answer 18

Draw them with their heads and tails joined. The resultant of the vector addition is the third side of the triangle

Question 19

How do you subtract vectors (-b^→ and a^→)

Answer 19

-b^→ is drawn in the oppsite direction. This gives us a^→ - b^→

Question 20

What happens when vectors are added and what does this mean?

Answer 20

They are added component wise and this means that the X components and Y compoments are added seperately to find the resultant factor

Question 21

A vector v^→ has components (3,4) and a vector u^→ has components (7,9)
Find v^→ + u^→
Find v^→ - u^→

Answer 21

(3,4) + (7,9) = (10,13)
(3,4) - (7,9) = (-4, -5)