### Short Answer

### 5.1 Vector Addition and Subtraction: Graphical Methods

- 108 cm, $\theta ={119.0}^{\circ}$
- 108 cm, $\theta ={125.0}^{\circ}$
- 206 cm, $\theta ={119.0}^{\circ}$
- 206 cm, $\theta ={125.0}^{\circ}$

- 108 cm, $\theta ={119.1}^{\circ}$
- 108 cm, $\theta ={201.8}^{\circ}$
- 232 cm, $\theta ={119.1}^{\circ}$
- 232 cm, $\theta ={201.8}^{\circ}$

Consider six vectors of 2 cm each, joined from head to tail making a hexagon. What would be the magnitude of the addition of these vectors?

- Zero
- Six
- Eight
- Twelve

Two people pull on ropes tied to a trolley, each applying 44 N of force. The angle the ropes form with each other is 39.5°. What is the magnitude of the net force exerted on the trolley?

- 0.0 N
- 79.6 N
- 82.8 N
- 88.0 N

### 5.2 Vector Addition and Subtraction: Analytical Methods

True or False—A vector can form the shape of a right angle triangle with its x and y components.

- True
- False

True or False—All vectors have positive x and y components.

- True
- False

- ${R}_{x}=\frac{{A}_{x}}{{B}_{x}}$
- ${R}_{x}=\frac{{B}_{x}}{{A}_{x}}$
- ${R}_{x}={A}_{x}+{B}_{x}$
- ${R}_{x}={A}_{x}-{B}_{x}$

- ${R}_{y}=\frac{{A}_{y}}{{B}_{y}}$
- ${R}_{y}=\frac{{B}_{y}}{{A}_{y}}$
- ${R}_{y}={A}_{y}+{B}_{y}$
- ${R}_{y}={A}_{y}-{B}_{y}$

When a three dimensional vector is used in the study of atmospheric sciences, what is z?

- Altitude
- Heat
- Temperature
- Wind speed

Which method is not an application of vector calculus?

- To find the rate of change in atmospheric temperature
- To study changes in wind speed and direction
- To predict changes in atmospheric pressure
- To measure changes in average rainfall

### 5.3 Projectile Motion

- $\overrightarrow{v}=\overrightarrow{a}t$
- $\overrightarrow{v}=\overrightarrow{{v}_{0}}+\overrightarrow{a}t$
- $\overrightarrow{v}+\overrightarrow{{v}_{0}}=\overrightarrow{a}t$
- $\overrightarrow{{v}_{0}}+\overrightarrow{v}+\overrightarrow{a}t$

In the equation for the maximum height of a projectile, what does ${v}_{0y}$ stand for? $$h=\frac{{v}_{0y}{}^{2}}{2g}$$

- Initial velocity in the x direction
- Initial velocity in the y direction
- Final velocity in the x direction
- Final velocity in the y direction

True or False—Range is defined as the maximum vertical distance travelled by a projectile.

- True
- False

- ${0}^{\circ}\phantom{\rule{negativethinmathspace}{0ex}}$ or ${30}^{\circ}$
- ${0}^{\circ}\phantom{\rule{negativethinmathspace}{0ex}}$ or ${45}^{\circ}$
- ${90}^{\circ}\phantom{\rule{negativethinmathspace}{0ex}}$ or ${0}^{\circ}$
- ${90}^{\circ}\phantom{\rule{negativethinmathspace}{0ex}}$ or ${45}^{\circ}$

### 5.4 Inclined Planes

- $\text{N}$
- $\text{m/s}$
- ${\text{m/s}}^{2}$
- unitless

- It increases with the increase in the relative motion.
- It decreases with the increase in the relative motion.
- It remains constant and is independent of the relative motion.

- When the magnitude of the component of the weight along the slope is equal to the magnitude of the frictional force.
- When the magnitude of the component of the weight along the slope is greater than the magnitude of the frictional force.
- When the magnitude of the component of the weight perpendicular to the slope is less than the magnitude of the frictional force.
- When the magnitude of the component of the weight perpendicular to the slope is equal to the magnitude of the frictional force.

- ${0}^{\circ}$
- ${30}^{\circ}$
- ${60}^{\circ}$
- ${90}^{\circ}$

### 5.5 Simple Harmonic Motion

What is the term used for changes in shape due to the application of force?

- Amplitude
- Deformation
- Displacement
- Restoring force

What is the restoring force?

- The normal force on the surface of an object
- The weight of a mass attached to an object
- Force which is applied to deform an object from its original shape
- Force which brings an object back to its equilibrium position

For a given oscillator, what are the factors that affect its period and frequency?

- Mass only
- Force constant only
- Applied force and mass
- Mass and force constant

For an object in simple harmonic motion, when does the maximum speed occur?

- At the extreme positions
- At the equilibrium position
- At the moment when the applied force is removed
- Midway between the extreme and equilibrium positions

What is the equilibrium position of a pendulum?

- When the tension in the string is zero
- When the pendulum is hanging straight down
- When the tension in the string is maximum
- When the weight of the mass attached is minimum

If a pendulum is displaced by an angle *θ*, what is the net restoring force it experiences?

*mg*sin*θ**mg*cos*θ*- –
*mg*sin*θ* - –
*mg*cos*θ*