Lesson 3: Vectors

Question 1

Vector

Answer 1

A quantity that has a numerical size, also known as magnitude, and a direction

Question 2

Scalar

Answer 2

A quantity that has a numerical size, also known as magnitude, but no direction

Question 3

Horizontal (or x) - component

Answer 3

The vector component given by:

Ax = A*cos(θ)

Question 4

Vertical (or y) - component

Answer 4

The vector component given by:

Ay = A*sin(θ)

Question 5

Magnitude of a vector

Answer 5

The length/size of a vector, written as the absolute value of the vector

Question 6

Pythagorean theorem

Answer 6

Question 7

What two characteristics are necessary to define a vector?

Answer 7

Magnitude and direction

Question 8

What is the magnitude of the velocity vector pointing directly down at 5 m/s?

Answer 8

5 m/s

Question 9

What is the resultant vector in Cartesian Coordinates for a trip that I took where I traveled 5 km south and then 2 km east?

Answer 9

(-5i + 2j) km

Question 10

What is the x component of velocity for a ball thrown upwards at 4 m/s at 30º with respect to the horizontal?

Answer 10

3.4 m/s

vx = 4*cos (30º)
= 4 (.86)
= 3.4 m/s

Question 11

What is the y component of velocity for a ball thrown upwards at 4 m/s at 30º with respect to the horizontal?

Answer 11

2 m/s

vy = 4*sin (30º)
= 4 (0.5)
= 2 m/s

Question 12

What is the sum of the vectors in Cartesian Coordinates?

A = (11i + 13j - 2k) m
B = (i + 13j + k) m

Answer 12

(12i + 26j - k) m

Question 13

What are the sum of the vectors in Polar Coordinates?

A = (12i - 5j) km
B = (2i - 12j) km

Answer 13

(22 km, 309.5º)