### 2.1. Define the term Vector
A vector is a quantity that has both magnitude and direction. It is used to represent physical quantities that are directional in nature, such as force, velocity, and acceleration. Unlike scalar quantities, which have only magnitude (such as mass or temperature), vectors require both magnitude and direction for their complete description. Graphically, a vector can be represented as an arrow, with the length of the arrow indicating the magnitude and the arrowhead indicating the direction.
### 2.2. Calculate the resultant force acting on the motorbike and rider
We are given two forces:
- The driving force produced by the motorbike: 500 N acting westwards.
- The frictional force acting on the wheels: 150 N acting eastwards (opposing the driving force).
To find the resultant force (net force) acting on the motorbike and rider, we need to consider the directions of these forces. Since they are in opposite directions, we subtract the frictional force from the driving force.
Resultant force:
[tex]\[ \text{Resultant force} = \text{Driving force} - \text{Frictional force} \][/tex]
[tex]\[ \text{Resultant force} = 500 \, \text{N} - 150 \, \text{N} \][/tex]
[tex]\[ \text{Resultant force} = 350 \, \text{N} \][/tex]
Thus, the resultant force acting on the motorbike and rider is 350 N westwards.
Next, we calculate the speeds of the motorbike and rider under different conditions:
1. Traveling against the wind.
2. Traveling with the wind.
#### Speed against the wind
The motorbike and rider travel a distance of 160 km against the wind in a time of 2 hours.
Speed is calculated using the formula:
[tex]\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \][/tex]
For traveling against the wind:
[tex]\[ \text{Speed against wind} = \frac{160 \, \text{km}}{2 \, \text{hours}} \][/tex]
[tex]\[ \text{Speed against wind} = 80 \, \text{km/h} \][/tex]
#### Speed with the wind
The motorbike and rider travel a distance of 160 km with the wind in a time of 1.67 hours.
Using the same speed formula:
[tex]\[ \text{Speed with wind} = \frac{160 \, \text{km}}{1.67 \, \text{hours}} \][/tex]
[tex]\[ \text{Speed with wind} \approx 95.81 \, \text{km/h} \][/tex]
In summary:
1. The resultant force acting on the motorbike and rider is 350 N westwards.
2. The speed of the motorbike and rider against the wind is 80 km/h.
3. The speed of the motorbike and rider with the wind is approximately 95.81 km/h.
These calculations give us a comprehensive understanding of the forces acting on the motorbike and rider, as well as the resulting speeds under different conditions.
